Did some research, and must correct an error in my above statement, and I'll update the article soon.
If you go to the linked BOM detailed table in my article, you will notice something.
The carrier is the same for all Ford RC 60's UP TO 98, and is the same as the GM/Dodge 4.10 carrier - namely part # 706040X.
BUT - you wil also note that the Ford RC60 was never offered stock with a ratio lower than 4.10 in those years. So I imagine all those stock Spicer gersets were not thick.
So, here's what I imagine happened - when afterarket vendors started making gears lower than 4.10 for RC 60s - they made the ring gear thick, so it could just go on the stock carrier. So if you bought aftermarket 5.38 gears for RC60 - they would likely be thick.
Now - if you buy an aftermarket carrier (i.e. locker) for your RC60 - I imagine, depending on where you buy it from, thay ask "year/make/model" and based on that would likely sell you the 4.10 down Detroit - that way - if you already had aftermarket lower gears, they would just go on the locker.
The problem you ight run into, is what happened to Insayn. You buy aftermrket gears first - lower than 4.10 and they're thick. Then you buy a locker by ration, not make and model, and naturally you'd think "I have 5.13 gears - I must need the 4.56 and up locker" but you get hooped because the gears are thick.
The 2000+ RC60- fords are offered with stock gears as low as 5.38 - but these are not thick and go on the same old 4.10 down carrier - they are thin and go on the same GM/Dodge 4.56 up carrier. The carrier break is 4.30 and down go on the 4.10 and down carrier.
I don't know if Spicer is the only manufacturer offering thin RC60 gears - I'll have to do some research.
Bottom line - you do have to match your carrier and gear set.