I have a '93 S10 Blazer 4x4 automatic with GU4 code rear end (3.08 gears) and an open diff. All stock everything and for the most part that's how I like it. I do mostly highway driving so 3.08 gears and the mileage they offer are perfect for me. I only ever do light off-roading on fields and camp sites. The most intensive thing I do with this truck would probably be pulling corollas out of snow banks. I would like to install a Limited Slip carrier to give myself just a little bit more assurance when pulling cars or driving on wet fields, but upon quick research I can't seem to find anybody else who has put a limited slip on 3.08 gears.
Looking at parts from summit, I see this:
https://www.summitracing.com/parts/dtl-912a317 - Eaton Detroit Truetrac Differentials 912A317
Which specifies that it "fits 3.23 and numerically higher gear ratios."

Is there some inherent problem with putting an LSD on 3.08 gears?
Would it physically not fit or is there some other reason?
Has anyone done something like this before?

 

I’ve got that exact set up on my truck; however, ​​​you didn’t mention if you’ve got the 8.5 rear or the smaller one?

When I built my truck, I swapped rears from a 5spd that had the 8.5 rear with 308 gears. I had the smaller open rear with 342’s before I did the swap.

I put an Eaton posi in the 308 rear, and had no issues swapping from G80 to the Eaton.