How to pick the correct lock ring removal tool

I have an (admittedly cheap) lock ring removal tool which is bundled with equally cheap red-handled chainwhips commonly sold on eBay:

This tool works great for installing and removing Shimano cassettes. I really like the fact that it has a 1/2" socket adapter so I can snap it on to my torque wrench.

I now have a bike with disc brakes and want to swap wheels. The aforementioned tool has the correct number of splines for the rotor, fits but only goes down about 1mm into the hole, so I’m unable to remove the rotor lock ring because there’s not enough purchase.

I’m looking at either Pedro’s 6460010 (lock ring tool with no center pin) or the Shimano TL-LR11. I’d like to avoid the Park FR-5.2 since it requires a 1" socket to fit on to a torque wrench, making it far too easy to fall out. The TL-LR11 says it is specifically for the SM-RT10 and won’t fit standard center locks, so I may be barking up the wrong tree. I have SM-RT70S rotors

Which of these tools would best suit my needs or should I look for something else? I’m also considering switching to external lock rings that require a BB tool, but would like to be able to remove the existing rings myself and/or use this tool help out friends in the future.