I am not an expert in these things like Ray. But, my understanding is 1-1/4" to 3/4" adapter is fine. If you insert a nipple to lock the cross tube (modified Reil version) you lose some flow so the 1-1/2" is preferred in that design.
I think a 5/64" (0.078") is too large of a hole for the orifice, my guess is you want something half that size or smaller. I made mine with 0.035" Lincoln MIG contact tips and they look like your tip in the pictures. The wire that passes through the hole is 0.035" and the hole is actually a little bit larger (or the wire would drag). You can see by the first photo I posted that that I'm running a bit on the rich side and a 0.025" MIG tip would probably be fine.
To use a contact tip in the Reil design you'd have to drill and tap the cross tube to accept the contact tip and ensure it's nice and square to the cross tube, so the gas is jetting directly down into the pipe. Drilling the right size hole is easier. Does anyone locally sell Dremel bits? They make small ones and a 1/32" should be common.
The setup I used looks like this:
Dan