How can I progress with researching/working with profs with a bad transcript?
Honestly, you should take a step back and focus on your coursework first. Research experience is great and often necessary for graduate applications, but it's useless if you don't have good grades in upper-level classes. Focus on showing that you can do well in courses before worrying about adding research to your workload.

Also, excelling in an upper-level class is the probably the best way to connect with a professor and get a research opportunity at this point. If you can get to know a professor a little through class and office hours and impress them there, then it's much easier to ask them after the class is over about research opportunities. The key, however, is that you have to actually impress them, and no professor is going to be impressed by a C or even a B in their class.

It also helps if you are willing to work as an unpaid research assistant or similar. Getting funded positions as an undergraduate can be very difficult, especially in math since it's unlikely you will do any real work. But unpaid positions can still be very valuable and are much easier to obtain.