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(where's that "eating popcorn while watching the show" emoji when you need it)
I think you're stuck with conceding the overlap and leaving a gap. Original corners rule unless you can prove them wrong somehow. Is your deed senior or junior to the parcel overlapped?
In California you can pull existing corners if you file a Record of Survey to show where they were.
Be careful that you are not the one "creating" the problem. Problems that small are sometimes created in the heads of expert measurers or GIS specialists, and fed to attorneys to get fat on.
If the original grantor is available and willing a correction deed might be good. But if the current owners aren't up in arms over 2' I wouldn't poke the bear. Determine where, in your proffesional opinion the law says the boundary most likely lies (in all states I have experience in it will say there is no gap), explain your decision in your survey, monument it, if possible record it, and then move on.
Instead of pulling it, you could drive it deeper so that it is almost impossible to detect with the locator.
Giving up the overlap to the south is easy. But how do you justify claiming 2 feet further north than what the north adjoiner has owned for as long as that pin has been in the ground? Quit claiming the south 2 feet to the southerly adjoiner fine. But you need the northerly adjoiner to quit claim the north 2' feet to your client. Once that is done it wouldn't bother me at all to pull the previous pins.
Unless my assumption about the north pin is wrong. If you are saying the north pin is already 2' further north than your clients deed, then I think what you are describing is a fine solution.
Describe them as witness monuments on your plat. Clearly mark them in the field and while you're showing them to the landowner drop a subtle hint about the high potential of them being troublemakers and how it'd be best if someone were to just rip them out of the ground.
If there were easy and automatic solutions, there would be no need for licensed surveyors to be involved.
All 4 corners were staked by the previous 20 year old survey.
I'm kind of leaning towards holding the four corners as staked.
If there were easy and automatic solutions, there would be no need for licensed surveyors to be involved.
Yes! And "easy automatic solutions" includes pulling older monuments because they don't agree with your measurements and/or record measurements.
All 4 corners were staked by the previous 20 year old survey.
I'm kind of leaning towards holding the four corners as staked.
That is a good solution, provided that your professional opinion of the boundary location agrees with those locations. Accepting 20 year old monuments is a good default decision; however; in this case the OP seems to think otherwise.
I am inclined to agree with him. The law tends to abhore useless small strips of "unowned" land. The overlap also needs to be evaluated based on senior rights, and any other applicable principles.
Edit: On second thought, I forgot the problem only 2'. Depending on the situation on the ground, just chalking it up to a harmless measurement error could be the best solution.
I would be looking very hard at occupation and reliance before making this decision...
Determine where, in your professional opinion the law says the boundary most likely lies (in all states I have experience in it will say there is no gap), explain your decision in your survey, monument it, if possible record it, and then move on.
This is my take as well. If you can reliably place the boundary where it is now (not where it supposedly was in the past) then do it and document it.
Monuments rule, until they don't.
There is no gap, there is no overlapp. Monuments rule,,,,,,,until they don't.
We just pulled one yesterday, sometimes you have to.
I'm an accept all monuments till I can't type of surveyor, if I accept them then they have no error in my opinion.
What type of monuments don't control?
It's a case by case situation.

If your monument is bigger than 2.2', there is no problem.
Issues like these makes me think that surveyors can be real shit-stirrers when they feel like it. My opinion is that the real boundary is where the neighbours agree it is. If two neighbours are happy with the location of the fence between their properties, no one should be able to disturb that peace for a silly intellectual exercise.
The sole point of this post is to gain opinions on what to do with conflicting corners when a conflict is discovered and asked to be resolved. This is not a situation of what to do with multiple pins at a pin cushion.
For this post responders should assume that it has been determined that a 75' wide parcel was INTENDED to fall in between two parcels that leave a 75' wide tract between them. Corners placed 20 years ago put all 4 corners 2.2' to the south. I can and will stake the new corners. I will "modernize" the legal by adjusting the lead-in and qualifying to adjoiners' corners. This solution leaves all deeds in agreement (within mathematical reason, +/- 0.15'), all parcels with deeded area/frontage, and doesn't not disturb existing occupation.
The only question I am asking is...what would you do with the old corners that have caused past confusion and might cause future confusion? Leave or pull?
All 4 corners were staked by the previous 20 year old survey.
I'm kind of leaning towards holding the four corners as staked.
That is a good solution, provided that your professional opinion of the boundary location agrees with those locations. Accepting 20 year old monuments is a good default decision; however; in this case the OP seems to think otherwise.
I am inclined to agree with him. The law tends to abhore useless small strips of "unowned" land. The overlap also needs to be evaluated based on senior rights, and any other applicable principles.
Edit: On second thought, I forgot the problem only 2'. Depending on the situation on the ground, just chalking it up to a harmless measurement error could be the best solution.
Yes, this is just a situation in a vacuum, since we don't know all of the details. I've said before that my inclination is to hold found monuments, until I can find a reason not to. So, yes, I'll pull out and use my professional judgment in this situation too
The only bar from a prior surveyor that I recall ever pulling was multiple feet from the original spot, horizontal and covered with about two inches of soil. It had sort of an "S" shape from having been hit by some sort of heavy equipment and left, unnoticed, where I found it several years later. The morasse cap was still intact.
The only question I am asking is...what would you do with the old corners that have caused past confusion and might cause future confusion? Leave or pull?
There is already a record of those monuments; they are still evidence, even if conflicting evidence, and I would hesitate to pull them in the absence of a boundary line agreement, boundary line adjustment, or court decision.
I would simply reference them (and reference them well, none of that "monument found SE of calc corner" BS) and explain their role in my boundary determination on the face of the survey. It would be best to gather the adjoining landowners and explain the facts, and your decision, to them before finalizing the survey.
If they are agreeable, then perhaps it's time to employ @murphy 's strategy of hinting that those old monuments will be nothing but trouble if left in the ground and leave it to the landowners.
If there is the slightest hint of a possibility of a disagreement, I would be hesitant to remove long-standing evidence myself, even if I am not holding it and have already referenced it.
@scott-bordenet given that, I would pull. Leaving has a higher potential for causing harm than pulling.