How much power are you looking to put through it? LSD important?
No real answers here, but some thoughts to chew on;
IFS from some 4X4s can maybe get you close. Example: Toyota trucks '86-? used a gear driven transfer case, so the front diff would work if flipped around to the rear. Stock ratios down to 4.44:1 (I believe). Cheap gears in all ratios, Detroit lockers, clutch LSDs, etc. Also, Miata diffs would take front ring and gear from B2000s, again, I think this is true.
I realize you were trying to buy something off the shelf, but with the cited prices, some of these junkyard pieces may do the trick. Also, look at Explorer/Expedition rear ends.
That BBC? is gonna need a strong diff. With that much torque why not pull against a taller ratio and go with a 1:1 final ratio in your trans?
My gut feeling is you are going to end up with a custom ratio in an otherwise common diff. It seems like the $ you are worried about for the diff are going to pale compared to the cost of other items you are must be using to get those numbers so if you consider the custom ratio in relation to your overall cost I can't imagine it being that bad. I would love to hear what battery/controller/motor you are using.
the 60's jag had a high 4's avail. frenchy may have one. they are close to bullitt proof and heavy, the C4 vette auto car had a dana 36 unit aluminum so lots lighter and the jeep people prob. have stupid high ratio's for a 36 . I THOUGHT MOST ELECTRIC CARS WERE USING 2 SPEED POWERGLIDES.if shorty cases were cheaper that could be for you.
I don't know what torque a Miata diff will take, but apparently the ring and pinion from the front of a 1st gen Sportage bolts in the Miata housing and has a 4.78 ratio.
Ford 8.8 has arguably the best aftermarket support and ratio selection. 2001 and up Ford Explorers and Expeditions were IRS and some of the later ones had aluminum pumpkins.
Otherwise there are IRS quickchange diffs which should be able to cater to your high numerical final drive ratio without issue.
A quick change rear can easily provide ratio's in the 6's but use up to 50 hp when you spin them fast.
All manual RX-8s had LSD rear ends with four-something ratios, with the 2009 cars having a higher ratio by a little bit.
If I read correctly, you need repeatability, not a one-off custom. How about a Curry 9"? In my circle track days I could get custom housing and axle lengths, floater ends, and any type of carrier and ratio you want. Have the housing ends cut as short as possible, axles to size and add a floater with disc brake setup. Then mount a u-joint flange to marry to the axles. Added bonus is less sprung weight at the wheel. Plus you have a clean housing to fab up the mounts.
Less attractive is the Dana 36 from the C4 Corvette. It can barely handle the torque from the early 90s LT1s. Plus you have to utilize the batwing for mounting and the front of the carrier is designed to use the C-channel mount to the trans. Limits your mounting options. Dana 44 is better but hard to find as the C4 guys all want them as upgrades from the Dana 36. Not sure what ratios and carriers are available.
Another possibility is the RE from a C3 Corvette. I've been out of that scene for too long, don't remember too much about them.
Finally, what about the 90s T-Bird? Didn't some of them have IRS 8.8s?
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