If you can stay 6" back form trim and corners.  

We took up the 1/4 round base trim of the baseboards which were like 6 inches tall so we could get a nice finish stain to edge and replaced that when finished

I don't like the heat treatment- specifically on older homes where it can warm the wood trim, windows, etc.

It’s inevitable depending on the breed and now trimmed their nails are.

I would work on trimming out even more of anything else extra in your budget.

Have all your trees trimmed, grass layed, bushes trimmed, caulk the outside of the house if it needs to get painted, maybe even replace rotten wood on the outside(facia boards, soffit), place gutters, etc.

Then you can keep the trim white.   

Seems high to me based on what you described as your scope of work.Are you replacing doors, trim, electrical, plumbing, roofing, windows, exterior doors, any landscape and concrete work?

They have a rental up there, and have some trees that need to be trimmed up.

Sherwin Williams Accessible Beige, Sherwin Williams White Ibis for trim are good starts.