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You can get a pretty good idea by just putting a mark on the input and output shafts and tuning the input shaft. If it takes a little more than 4 turns of the input to get 1 turn of the output you most likely have a 4.11
I think a 4.11 is too much for the highway unless you have an overdrive transmission. I'm going to put 4.10 gears in my diff but only because I'm using a 6-speed trans with overdrive in the top 2 gears.
The numbers you listed are definitly for a 4.11. The ring gear is 3733908 and the pinion should be 3885945. A 3.70 gear should have 3737957 on the ring gear. See if you can count the teeth on the pinion. For a 4.11 it should be 9 and a 3.70 should be 12.
Back in the 60 and 70s 3.55 to 4.11 gears were normal and the ygot driven all the time. 3.55 is a good combo gear for in town and highway. I ran a 4.11 gear with my M20 and it was steep on the highway. The 3.70s were better but a 3.55 would be even better. inow run an OD with a 3.70 gear. The OD brings it down to a 2.51 gear. You should not overheat providing everything in the cooling system is in good shape.