Possibly. Wouldn't hurt to actually measure pinion depth.

 

Is there a way to accurately measure pinion depth without buying/borrowing the "contraption" that the service manual and vids I've seen say to use?

 

You are "assuming" that the new bearings are exactly like the ones you removed. Depending on who made them they may differ slightly(closer or farther away) from the ring gear. So if you can't get the correct pattern moving the ring gear moving the pinion is the only other option. Get a set of various thickness shims and then put the smaller ones in first. if you cant get the correct pattern use the larger ones. With the correct combination you will get the pinion where it needs to be.

 

No. You need the proper tools.

 

Pinion depth tools are fairly rare. When I went through training for Randy's/Yukon I was in a room of experienced gear guys and the consensus was none of them used a pinion depth tool......basically because 99% of the time you're referencing off what was already in there and when you purchase new gears they're scribed to let you know if you're likely to need to add or subtract a few thou.

I'm not saying pinion depth tools don't exist or can't be useful -- just that they're more of a specialty tool even within a specialized field.