Thrust washers are a common problem on the later motors, that have only half as much thrust bearing surface as the TR2-4 motor does, but I've never seen or heard of a problem on a TR3. Mine weren't too badly worn even on the engine where the rod bearings were worn all the way into the steel backing (previous owner apparently didn't believe in oil changes). I use compression braking frequently and I've never worn out a thrust washer or bent a push rod. Synchro rings I have worn out, but only after a lot of miles. (Got perhaps 150,000 on the current set, guess I should have changed them when I had the OD apart last.)
But, using compression braking does make the engine more apt to die, because the cylinders and spark plugs cool off and possibly even load up a bit with unburned fuel. The engine is basically just barely running if at all (which is why exhaust emissions are so high and many emission setups include a means to hold the throttle open a bit to keep it running or else add plain air to make sure it doesn't).
So if it dies like that (and mine does at the moment), I take that as an indication that it needs a tune-up. New plugs, points condenser; plus adjust the ignition timing, valve lash, and idle mixture. Also check that the carb pistons move absolutely freely (except for the action of the dashpot of course) and land with a distinct click. If they are dirty or the jet centering isn't perfect, that will also make it want to die sometimes.
As a side note, I've discovered that on the carbs I'm using, the dome-to-body fit is loose enough to mess up the jet centering if I R&R the domes. So now I install all 3 screws loosely, then turn the dome clockwise for final tightening, so it always returns to the same place.
If you've been through all that and it still wants to die, you may need a little bit higher idle rpm. Almost any sort of engine modification, like larger liners, more compression, lighter flywheel etc will need a bit more to keep it running. (I have all 3 of those.) The engine I had before with the "3/4 race" cam didn't like to idle below about 1500 (and was a bit lumpy even there).