That's one of the reasons I'm reluctant to abandon TBC. It stores the raw GPS observations. You can do about any projection you chose and export coordinates. You can set it to any projection and import plane coordinates. You can have a projection going and import a dc file set in another projection and it handles it just fine (takes the raw Real GPS values and displays them in your projection). You can change the projection without any import or export, just do it. The latest version is supposed to have drafting capabilities but I haven't tried it yet, supposedly a big step toward a replacement for Terramodel.
OK, I'm not stuck on Trimble but unless the others have these capabilities I'm not changing.
A geodetic database office program should store all the raw data observations for a point and then be able to project these points in any system and export the result. It should work in reverse also. A point export or import should have a meta data file attachment that tells what the input or output data and projections where. The program should work on an office computer and be able to have it all backed up in the cloud.
Again. Point data can be re-projected fairly easily. Vector data (line work) is a bit different animal. I know [REDACTED] geographic calculator does it but I'm not sure how it handles curves.