Tyler - To answer your questions:
"1) Can I really pick up AO-7 with my antique Allied Communications tube receiver if I put the preamp at the antenna?"
1. Yes. You should be able to even use the preamp at the receiver, as the sky temperature is pretty high and transmission line loss is not too great, particularly if you use RG-213 or equivalent. I haven't worked Mode A on Oscar 7 this time around, but 25 years ago I received it quite nicely with an old FT-101E with a CB preamp of unknown pedigree at the receiver. The antenna was a loop tacked to the ceiling of the shack with about 10 feet of RG8X. I never had trouble hearing the satellite. This was in LA county, so local noise was pretty high.
"2) How much EIRP do I need on the uplink? Can I use my IC-706 barefoot, or am I looking at a Mirage amp? I think the 706 puts out 50 watts on 2 meters. I'd probably be using a 3 element beam for uplink with something like 9? db gain. I think I saw something like a 90 watt EIRP would be sufficient for the uplink."
The 706 barefoot should be fine, at least on CW. I used to work the satellite with an old Ameco TX62 feeding a 1/4 wave ground plane at the end of 50 feet of RG8X. That is probably 20 - 25 Watts EIRP. I had to turn down the drive on the TX62 to march the beacon, so I was running less power. I suspect that you can run SSB with your setup no problem though. Just remember to keep your downlink signal weaker than the beacon.
"3) Do I really gain a few more db in gain if I suffer while I put the antenna up in the supercold weather here in PA, or is that just an urban myth? :-)"
That is an urban myth. I know, having installed a 160M antenna in -10 F weather in SD one year as a foolish youth. - Dr. Megacycle KK6MC/5
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-- James Duffey KK6MC/5 Cedar Crest NM 87008 DM65