I am struggling to efficiently add blocking to 16" stud bays when I can't end nail through the other side of the stud. I have a full-size nailer, a palm nailer, and a hammer or two--but not a lot of experience with any of these. What are your tricks?
Since you have a palm nailer, use that. However, I think it is worth mentioning that in lieu of a palm nailer, an electric screw driver, (which is more commonly owned by DIY folks than a nail gun), is easier to use in this situation than a regular hammer and nails.
Oh, and the way to nail them in is to stagger the blocks.
Edit: Please excuse me; for some reason, I thought you were having space issues (I misread). As everyone else said, use the regular nail gun.
Use the full size nail gun.
Cut the blocks so they fit tight.
Get them into a spot where they're about 1/4 inch from where you want, because when the nail gun goes off it will push.
Do one toenail through about 1 1/2 inches of the block into the stud.
Fine tune it with your hammer and then do the rest of the nails.
Support the other side of the block with the handle of your hammer if you have problems with them moving too much. Do every other one first, so you don't have to toenail them all.
There's no problem whatsoever with angling your framing gun nails slightly to face nail through the studs and into the ends of the blocks. Do this if you prefer the blocking to be on a single line for sheathing seams or whatever.
Otherwise, stagger them on a centerline as Ben Welborn suggests and again face nail them with the framing gun.