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I was in the same boat as Frank.
My '3.88' was actually a 4.12.
But, I think Frank didn't find out until after his new tranny was spec'd and built. Thinking he already had a 3.88 (and that that was geared too low), he ordered a 3.44. What he really needed all along was a gen-u-whine 3.88, but he found that out too late.
I was a little luckier. We were able to figure out the actual gearing inside the old box before ordering a new one. Once the old box was torn down, it turned out it contained too many substandard parts, so instead of rebuilding it we just built a new four-speed from scratch, with 3.88 and .89 top.
My 2024cc is no monster, so I eventually solved the problem with gearbox number three - a five-speed - and this has worked for me. It's got a 3.88, and the old .89 top gear, but the new fourth gear is a 1.14, and that is perfect for hilly, twisty two-lanes, between about 40 and 55 (where I do most of my goofing around). In this gear, there's enough grunt to pull up pretty steep grades at surprisingly low rpm's.
I usually don't shift into fifth until about 50 mph (around 2400). I can sometimes carry the gear down to around 2200, ghosting along really quietly at 45 mph, but downshift to fourth if I need to punch it.
There are many ways to make these ancient engines drivable in modern times, but they all cost money.
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