X2 on the checking bearing. I've done that, it works. BTW, I have an inexpensive pinion depth tool listed in the classifieds...
Gearset should have a marking on it indicating pinion depth measurement. If it's there, start with that and check.
If you don't have the correct bearing puller, you can certainly cut the old bearing off with a cut off wheel. Just be careful not to damage any important machined parts. For final install, you can knock it down with a steel tube that matches the inside diameter of the bearing cage and whack it with a hammer until it's fully seated. Not the best way to go about it but it works.
Do you have a holding fixture? A dial indicator to measure backlash? Inch pound torque wrench to measure pinion turning torque? Big torque wrench to tighten the pinion nut? No small feat to crush the sleeve. How about marking compound to check your pattern? Seal/race drivers?
It's tough to do this properly without the right tools.
