Very good points you raise.
What should you keep in mind when swapping components from one frame to another?
Fit.
What do you need to measure?
Trial and error is just as quick.
What specs and parameters do you need to know?
Type of headset (threaded or threadless) Seems like you have a pretty good handle on what you're in for.
Stuff like that, feel free to comment.
And me, so shy about that kind of thing.... 
A 1997 GT Edge road bike, 7075 aluminum frame, 130mm rear dropout spacing.
He says I'd have to use the Centurion bottom bracket.
Should be fine. You can pick up a new cartridge one for under $30.
It will come with the fork and headset. I think the fork was aluminum.
Having the headset is good. The ones I've seen use 1" threaded headsets, so you can swap the stem/bars right over. Don't even disassemble them. Your brake cables/housing will likely be too short.
I'll probably price a new BB but will need to figure out what the GT requires.
See above. Standard English threaded double square taper, cartridge will be fine.
That way I wouldn't have to take the BB off the Centurion.
That's nice for the next guy, too.
I will assume the stem and handlebars will swap over but would need to measure the steering tube to be certain.
See above.
Seatpost may or may not swap over, measurement or online second search required.
Just try it, chances are it wil fit. 27.2 on the Ironman.
Cranks/chainrings should swap over but I will have to verify chainline alignment since I had that issue once with a MTB frame swap.
Worry about that once you have the wheel set figured out. Swap the crankset over and don't worry about it until later.
Front deraileur may or may not swap over depending upon seattube O.D.
Aluminum that age is generally 31.8, your Ironman FD clamp is 28.6. Check when you swap, then let me know, I've got a 31.8 105 if you need one.
Rear deraileur should go on okay.
Yep, but it will need to be adjusted. If you use a spacer, you're 2mm too far out, across the range.
Wheel set should be okay except for the spacing issue in the rear. I suspect with the 130 spacing that the GT had either 7 or 8 cogs on back and I'm not a fan of using the skewer to pinch out a 4mm gap.
Don't pinch, use a spacer, 2mm each side. This should solve the chain line problem, too. 9/10 times, no problem.
You may also need longer shifter cables if the frame is bigger. I think it will go well, and again, I've got a 31.8 105 FD you can trade for your 28.6. He may have the same problem, and you switch with him! You'll need longer rear brake cable and housing, so you can pick a new color, if you want. Same with the front brake. Get the bike together, and then address fit.
Good luck, have fun, wish I was there to help.
