Mathematics MS/Msc to become more competitive for new cycle

Hey everyone!

So, I'm a VERY non traditional student (military). I didn't know much about academia when applying to PhDs this cycle, and I've certainly learned a lot! I'm decently competitive, and I got into 1 fully funded PhD! But there are other schools that I want to try for again. I did apply to some masters/msc programs as a back up and I got into essentially all of them. I am still waiting on the Cambridge MAST-III acceptance/rejection to come.

Now that you have context, my question is should I go for a master's program a great school to re-apply for next cycle? In particular, is the MAST-III program (assuming I get accepted) worth it to get into a T10-T20 math PhD?

I want to be clear that my motivations for a PhD are absolutely advisor and research fit, it happens to be that 2 of the programs with extremely strong match are IVs that rejected me...

Be brutal with the feedback! Thank you all :)