Question.

For forming a .327 diameter, .140 high round head on a 3/16" diameter rivet, what length should I have extending beyond the surface ?

I purchased from McMaster Carr:

#97300a677 rivets
2" long
3/16" diam
head is .327 diam, 0.140 high.

The 2" length is more than needed for use in the rear trunion....but I need to know just what length to cut it to , to leave enough material to form a nice round head when squishing the rivet.

I don't know the exact dimensions, but I have found that leaving 3/16" of rivet extending past the receiver will leave just the right amount of material to form a round head exactly like the other side of a standard rear trunnion rivet.

However, I used the correct metric rivots that are slightly smaller than the 3/16" rivets you want to use.  I believe you will have to drill out the trunnion holes to fit the larger rivets.

I have found that is is better to start the head formation with light taps from a hammer.  Then I use a small piece of metal with a divot in the press to finish the head.

I don't have a plinker's jig...

if you can find 3/16" X 1 1/2" they are good for AMD rear trunions. you do need to drill them out with a 3/16 cobalt though.

\so, to answer your question, less than than 1/4" sticking out on a 3/16" dia rivet. and more than a 1/8