You are correct on all accounts. Let me just say that trying to get the sound you’re getting from your Mark Bass will be extremely difficult, mainly because your amp was designed to do tgat exact thing and your PA was designed to cover a wide spectrum of frequencies, not focus on one area.
If you can do it, please try using a HPF and compressor between your tech 21 and the board. I would start with the HPF at 100hz and some mild compression.
As I mentioned in a previous post, you ought to set-up the sub and one PA Speajer aimed back at you. Then you and the drummer work on the bass signal and the bass drum to get them manageable abd able to coexist in the mix.
You would orobably be best to work on your sound first, then once you have thst at an acceptable level and tone, add the bass drum.