First and foremost, I'm glad you figured out the installation of the adapter from the first picture to the second!
I wouldn't worry too much about what drive style the screws are/were. I guess the advantage to Philips in this case is that it's hard to over-torque them? I would've expected socket-head (Allen) like Mr Gasket uses, but as long as they're tight you should be OK.
All the mixture/idle speed adjusting needs to be done with the vacuum advance disconnected and, as I've said several times, the engine fully up to temperature. Using only the mixture screwss, get the vacuum as high as you can with the idle set at the desired RPM. Add in a couple of degrees of timing; if you're at 10° now, try 12 or even 14°. The idle should rise, which you want to back off with the idle
speed screw to your original RPM reading. Now mess with the mixture screws again and see if you can get any more vacuum.
I don't know if I've mentioned this in the past, but the mixture screws should be at very-nearly identical adjustments. In other words, if you move the left half a turn and get 0.5", switch to the right screw. Turn it the same amount in the same direction
prior to turning the left any further. When turning the first screw has no effect, turn the other the same amount. If there's no change after that, turn both back to the previous setting. It's a bit of a tweaky process, but one that once you're used to it doesn't take long a'tall. When you've got it nailed, you can come over and do the 830 Holley on Agnes... it has
four mixture screws.
The fact that you gained 2" is quite encouraging. That means the carb swap was justified. Further justification comes from the fact that apparently it's not dumping fuel anymore, which aligns with my guess that the pump is probably OK. I think you'll be happier with the Thunder Series, too.
You're very close, young man. If you hit a setback now, just go review one of the
older pages in this thread, and look how far perseverence has gotten you. Driving this thing is in sight now!