First of all, congratulations on the new biz, it's a fantastic feeling to get rolling.
You've gotten some really good advice here, so I just wanted to add a few things. If you are getting signed contracts then they want to cancel, I'd talk to my attorney about how to word those contracts. Maybe put a clause in there about cancellation and billing time spent.
It seems like you know who you're losing out to on these deals.... could it be a burned bridge situation?
Also, I would review your website... some items need to be tweaked for alignment!
I would really take Bruce Small's advice to heart, he knows that market well, and how to run a lean survey biz!
I run into this all the time, My biggest competition is semi retired guys looking for golf money. I refuse to lower my prices because I value my license since I'm basically 1 of the 10-ish PLS' under 40 in my state, so I will be doing this for a while. So they book months out and I can get to a job in 2 week and I get the proper amount of work to keep my quality much higher than everyone else.
I was told early on it takes 2-3 years to get past the bottom of the barrel jobs and build up enough notoriety for your business to take off, I'm almost 3 years in and it appears to be true.
I'm mostly a residential surveyor so people will shop around to save $50 which sucks, But occasionally I get sent other peoples surveys and they are indeed producing a product that just barley meets local standards. Keeping my prices higher allows me to take less work and make a fair living, which is great for me. Now if you have employees to keep busy.... I can see grabbing as much work as possible, I just wish it wasn't at a 25-33% discount.
Hang in there, Competition cant take all the work, and they will start pissing people off. Everyone that calls me thanks me for answering phone, and enough of them value it.