First off, welcome to bikeforums! Secondly, as someone how has tinkered with 27" frames and newer parts, let's see if I can get you through some of the pitfalls which are awaiting you:
#1 biggest problem you are going to face is the brakes. Older frames had a longer drop between the brake bolt and the rim to allow for larger tires, fenders and all that jazz. Even if you keep 27" wheels you are going to need at least 'standard' length brakes which are typically approx 47-59mm length. I would nearly put money on the fact that you have a set of short reach dura-ace brakes who's max reach is ~49mm. If you get a Carbon fork, it will fix this problem for the front brake, but you are still left with the rear to deal with. There are drop bolts (if you can find them at usually around $40+ each) that will help.
#2: your carbon fork idea. Good idea, just know that you will need one with a 1" tube, which will most likely be a threadless design. Which will need a threadless headset. There will likely be a minor change in the bikes geometry with the new fork that you need to be aware of. I won't pretend to know much about that and hopefully someone else can give some possible effects of this change.
#3 as far as the crank, I haven't worked on these new DA cranks and bottom backets, but some searching on google and/or these forums will likely yield some information on what is needed.
#4 last thing that may be an issue is if your vintage steel frame has downtube shifter bosses for the brifter cable adjusters. I know that the Shimano Golden Arrow shifters (which are about $22 at loosescrews.com) have a clamp on boss design that may get you around this. I haven't tired so can't say for sure, but it's an idea.
If you get the golden arrow shifters and end up not using the levers - let me know, I'm looking for a spare set without the clamp band.
-- slaps forehead, something else you need to be aware of is the difference in rear drop out spacing. New 9/10 speed stuff is going to want a 130mm spread and your frame is likely 120 or 126mm. Do a search for cold setting a frame on the boards. Lots of info on how to fix this since you have a steel frame. Sheldonbrown.com is another wonderful resource on anything cycling related!