Thomas: don't overthink things.  A 38 X 11 with a (by Rivendell standards)
skinny 38 mm tire will give you a 97" top gear. FWIW, the top gear on the
only bike I own with multiple gears is 89" (42 X 14 X 29.5") and I never
use this. The other 3 are fixies with, seriatim, 76", 70", and 69" gears,
and I rarely overrun these.

If you replace the 38 with a 40 or 42 or even a 44, everything will remain
pretty much as it was before, except that all the ratios on the "big" ring
will be bumped up correspondingly. But a 38 t to 44 to jump is still, in
the cosmic scheme of things, Not a Big Deal. At most, you will have to add
a link of chain.

Patrick Moore, perversely and very deliberately shifting 42/28 X 14-28 (10
speed) with Bar Cons pulling a short cage DA 7410, in iconoclastic ABQ, NM.
(Oh: The 42 and 28 are in middle and inner positions; the outer has a
guard; 46 or 48, IIRC; forget nominal teeth, but way bigger than usually
required. And the reason for the exceptionally big guard is that I filed
off the outer stop on the 7410 fd. (And for why? Long story; basically to
get it to shift to the outer on a modern mtb triple, since replaced) and
the excessively big guard keeps the chain from overshooting.)

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