between the choke plate and air horn w/choke on...should be about 1/10th of an inch. You can adjust it with the little brass nut at the top of the choke plate actuating rod. Sounds like carb mixture is not rich enough to start w/o raw fuel being poured in there. You also have to check the secondaries to make sure they are closing all the way at idle. There is a little nylon peg sticking out from the choke adjustment lever, on the pass. side of the throttle shaft, that forces the sec. closed. These pegs are subject to failure...may be the hard starting/high idle problem. I had to make a new one using a small machine screw and nut, then pressed a thin-wall brass tube over the screw threads to get the actuation just right. Ace sells thin-wall brass tubes which can be used to make the vents. You need the 7/32 size, cut to 1 3/8 length. Cut a slot in the end, then press them in w/Loctite...after polishing, of course.
You mentioned throttle shaft play...I was surprised at how much play you can live with. Plenty of cubic inches to "hide" some leakage in that area I suppose. But since the whole carb/mani is already on the bench, why not get a good kit(Motorcraft CT-191A) and go through the whole carb? With that kit, you'd have to buy the secondary diaphragm separately. It'll also give you a chance to record the 2 booster codes on the underside of the boosters. Make sure the power valve cover is flat as I've seen MANY distorted by over-tightening. You're gonna need to remove the top anyway to adjust the fuel level. With a brand new rebuilt engine, you want that baby to fire instantly and run at 2,000 to 2,500 RPM for 20 minutes so getting the carb right should be your goal.