Centrelock tools

I have a new bike equipped with SRAM rotors. They are secured using centrelock with external splines - like this:

Can anyone recommend a tool to remove these? I have 2 tools, neither of which work:
https://ride.lezyne.com/products/1-st-exbbt-soc-v108?_pos=2&_sid=2c7f548c6&_ss=r This is too shallow and won't fit over the protruding axle to engage the lockring
https://merlincycles.com/en-gb/pedros-bb-wrench-shimano-16-notch-99358.html This is too shallow and I cannot get a proper grip on the splines with it.

The only options I can find that looks like they would work are:
the IceToolz Disc Brake Lockring Tool, #M082 https://icetoolz.eu/en/icetoolz-disc-brake-lockring-tool-m082/a5840 but this is not in stock anywhere.

Or the Park Tool BBT-69.4 https://www.parktool.com/en-us/product/bottom-bracket-lockring-tool-16-notch-bbt-69-4#tabbed-section but I'm not sure if this is deep enough to fit over the axle and cannot see any dimensions online.

I can't believe this isn't a common problem but there seems to be very little information online to assist with this. Can anyone recommend a tool to do the job, preferably something made of steel rather than aluminium?