My undergrad GPA was not as bad as yours but I was also young and crazy and in the habit of droping courses post limit. The thing is they did not count in my GPA but appear in the transcripts, so it looks really ugly; a bunch of really good grades mixed with Fs. Weird. But I did get it back together for my Masters and made it to the Ph.D with full funding and merit Fellowship! Try to focus on what really matters; your statements (proposal and writing sample) and the profs (the ones who recommend you and the ones you plan to work with). I am not shy when comes time to ask for advice (to everybody I can get my hands on in the field, respectfully of course, not like a sociopath) and it paid well. I certainly would not waste time doing another Masters (I think this will just look weird, unless you enter a 1 year program that leads directly to the Ph.D). First, put together a short research proposal, then ask your former profs where they think you should go. Do your own research via internet. Then, send emails to profs with similar interests with just a short paragraph of what you want to work on and ask if they could meet with you, and/ or redirect you elsewhere. If they redirect you elsewhere, send the next email saying that prof recommended contacting him/her. Name droping, when done tacfully can help. As long as it is done subtely, without pressuring them and without making anything up. Keep the focus on the research always.
If you are still doing your masters, try to TA if possible.
Good luck.
Ps. Some of my former profs admitted having terrible grades during their undergrad. Even the ones coming from the best Uni and who rae really top in their field