You are correct about the 34" door. To trim one down, it would need to finish out at about 32 5/8" to fill the jamb properly, actually 32 11/16" at the widest but anyway... you will not have enough material to fasten hinges or the latch for the knob.
If you set a 32" door in the opening, it would look really bad, at least in my opinion, with a huge gap on the latch side, and the latch would not want to work with out something extra added to it.
Adding to the jamb is an option, ten you may have issues with the finish matching the existing, the trim having a difference around the jamb, one side now being way different than the other.
My fix, if you have the capacity, is to add 3/4" to the door. If you can get it ripped to 1 3/8 wide and glue it to the edge, holding it in place with screws, until the glue dries, then you can remove the screws if you choose. Use filer to flush up the joint and sand flush. This is an over simplification, the added piece will not want to follow the door exactly, so it will take some finesse to make it look good. Filler sanding and paint will do the rest.