How to pick the correct lock ring removal tool
The limited engagement you speak of is a quirk of some hub and Centerlock lockring combinations. It's annoying. You are correct that if you want, you can probably eliminate the issue with the kind of Centerlock lockring that uses an external BB tool. To my awareness there's not really another way; when I've seen this it's not a tool compatibility problem as such, but the hub has something going on that would block any conventional lockring tool from getting in far enough.
To do it with the tool you have, use a lightly clamped QR skewer to hold the tool on, and then turn it with a big adjustable wrench. That should be able to overcome the limited purchase if the end of the splines are still in okay shape from prior attempts.