[MR_GRUMPY]

If everything that you say is true, you need to find an ultra six freewheel. They fit 120mm spacing.
Good luck finding one that isn't worn out.
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[MR_GRUMPY]

This frame must be 126 spacing.
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In 1988 they were beginning to make 130mm frames.
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[MR_GRUMPY]

If the shift levers are not indexed, you can use an ultra 6 speed freewheel like this

http://www.ebay.com/itm/NOS-Suntour-Pro-Compe-Ultra-6-Speed-Freewheel-14x23-/270435211504


If the levers are indexed, the components were made for a bike with 126mm spacing. Since the frame is carbon with aluminum dropouts, you can't spread the frame to 126mm.
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[MR_GRUMPY]

120mm spacing was the standard before 6 speed freewheels were invented. Almost all steel 120mm spaced frames could be spread to 126mm, by bending the rear triangle, and then straightening the dropouts with a dropout tool.
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[MR_GRUMPY]

Most American made bikes were spaced 120mm, with 27" wheels, until the early 80's.
If you wanted a "racing" bike with 700c wheels, you needed to buy an Italian frame.
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[MR_GRUMPY]

You're stuck with either a 5 or an ultra-6 speed freewheel.

Good luck finding a 5 speed "racing" freewheel (13-22) or (14-24)
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Ultra-6 is going to be even harder to find.

It's even hard to find "racing" 7 speed freewheels anymore. All I have left is a 12-18 and a 13-24 Sachs, and a 12-19 DA, in good shape.
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