Update on this - there seems to be some confusion around how to install this seal. I was provided some pictures of the depth specs for this seal (posted above) by a mechanic in the UK who personally owns a variety of Toyotas (MK4 Supra, Starlet, MKI Yaris). Those images show the seal being installed with an SST tool, and there are other threads on the forum indicating an SST tool is required. Despite all that, it doesn't appear that using a tool is the end all method.
There is a sleeve area on the transmission casing where the axle seal sits. Just behind that space is a step/lip. You do not want to push the seal in beyond that lip and you can get the seal into the sleeve evenly by hand relatively easily. Using a tool, like a large socket or bearing press, seems to increase the chances of both damaging the new seal and pushing it past the lip in the transmission casing. In our experience, the hand method provides more control with less risk of damage to the new seal. Without having seen the official SST tool, I assume it has a stopper/safety that pushes the seal in to the desired depth and won't let you push it further, but the SST tool has been discontinued and the part number now calls up a bearing press tool, which does not have a stopper/safety.
Pics of the transmission casing and hand pressed in seal below. Several test drives later and not a drop of gear oil on my garage floor. A former forum member I consulted with while doing the job also found
this YouTube video of the seal being installed on C50 transmission in another Toyota model. That video also claims that simply pressing the seal in by hand is the way to go. Lastly, I know a mechanic who we called while doing the job who also said the seal just sits in the transmission casing sleeve and can be pushed in evenly by hand. Hope this helps someone someday!