IMO you'll be better off to pull the box and do the work on the bench. You've already got the apron off, and once you've got the stator tube out and the upper column disconnected (which you'll have to do anyway), the rest is easy. I just went through this with TS13571L, and even though I decided not to update the box, I was still glad I pulled it just to get it adjusted properly.
It takes a strong puller to remove the drop arm as it's a splined locking taper, which is going to be difficult if not impossible while working in the limited space under the car. Also best to remove the worm first, before pulling the drop arm, so there's no possibility of slamming the pin into the worm and damaging either one.
Again IMO the easy way to remove the seal is to push it out with the bushing, but I don't think you'll be able to knock either one out with a punch without risking damage to the box. And if it's tired enough to leak, it's probably also tired enough to need a new bushing. Some all-thread, nuts, flat washers and a socket to pull the seal & bushing into works a treat, though.
On reassembly, be sure to check and adjust the shim pack before installing the top cover (to ensure that the peg is not putting ANY side force on the worm while checking the end float). I've been using a dial indicator to check end float (add shims until you can measure some float, then subtract shims to equal that); but it could probably be done by removing all the shims and doing a trial assembly with the bolts just finger-tight. Adjust them until you get an even gap all around, then measure the gap with feeler gauges and install that many shims (including the gasket thickness).