I usually look on eBay for the old stock stuff….and I’ve used Mouser. 

Just changing the gears from 3.00 to something like 3.50 would wake it up without doing any engine work........doing those other mods without changing them you might still be not to your liking, it's a heavy car and right now it's got freeway cruising gears in it.....

Wish I could offer more for that but my PPL was back in 87.....given your attention to detail you've got this, best advice I can offer is to relax, go SLOW and methodical, nowhere does anything need to be rushed.  If you think you missed something, as long as the ride is going keep moving forward.  (I fly for a living, so a checkride is a yearly thing, if you feel rushed or jammed up take a deep breath to relax, calm, and help slow the situation down so it's manageable......one task  at a time)

I used studs on mine.  Keep in mind, the holes in the pan aren’t spot faced (at least the ones on mine weren’t) so some don’t exactly sit flat.  I’d recommend using ARP nuts with the flange, there flange is more narrow and fits better in some of the locations……I didn’t have any issue getting a socket on any of them.

Should be a tag on one of the bolts……
https://www.stangerssite.com/steeringboxtagdecoder.html

What are you wanting in a modern trans, 5 speed with overdrive?  Nothing is going to be bolt in per se, lots of changes will be required.  Me personally would go with a TKX,  2.87 first and .68 overdrive.  If your cam is rowdy and it doesn't like lugging along at 1800 or so you'll want 3.91 or 4.11's in the axle.  Otherwise 3.50 would be the tallest set I would use.    I wouldn't put the 4 speed back in my Mustang for anything after having the 5 speed in there......but, you will need a new clutch disc, a spacer adapter for the trans to bellhousing, new driveshaft, not sure how much you can move the crossmember around on the Comet chassis but it will need to be moved back, also not sure if you will have to cut the tunnel, or modify the piece on the floor where the shifter comes through, although you can buy the shifter tunnel hump new and cut away.....driveshaft will need to be shortened.  American Powertrain and Modern Driveling both offer kits, but I think you are better off sourcing a lot of the stuff separately and getting just the stuff you want.

I think your rear brakes aren't adjusted as tight as they should be, on mine it holds the car fine, can only push it about halfway down.  All the components are newish, even the cables. Maybe try tightening the assembly where the cables meet, and give the star wheel on the adjuster a couple clicks on each side......