I'd say talk to Thai Elite directly. When I did mine I applied through the "top google result". Didn't even realise it was an agency of some sort (worked out nicely and didn't cost anything extra.)
I got mine in May. And I have zero regrets even if I could've milked the amnesty (which wasn't clear at that point.) The amount of anguish spared and having to deal with immigration, is already great value to me.
A little over a month seems a little tight to obtain Elite. I would apply immediately (which won't cost you anything) and start talking with them directly while waiting for approval.
As others said, best to talk with them directly. AND the Thai embassy. Getting approved will probably take 3-4 weeks. But then comes the payment phase. At that point it would be nice to know that there's at least a chance one could get on the list to enter the country (which is an embassy matter.) Best of luck!
That's good advice, I think :) But I'd bet the question was about CW vs MTT (no energy to type those names again. And yet somehow ended up typing even more.)