From industry in CS to pure math Ph.D/masters

[FtYoU]

Hi everyone. I am in the process of applying to graduate school and since their are multiple different deadlines, I would like to have some feedback on my unusual profile to maximize my chance toward my ultimate goal to be a Ph.D in pure mathematics (logic track).

I went to an European school 8 years ago with an undergrad focus on mathematics and physics. I enrolled for 2 years in the preparatory classes in France which are really competitive classes to integrate the Grandes Ecoles (i.e Engineering schools). After this I went to a Computer science Engineering school for the remaining 3 years.

Following all of those I had the incredible opportunity to join a big software company. My official position is R&D in machine learning and computer vision. During my 8 years in the company, I have always been passionate with pure maths but with my workload, I figured it was enough and I wanted to do research in maths as a full time job. The route of the Ph.D seemed the most logical to me, but after reading a lot, and analyzing the current and previous successful students, I have come to the realization that I have nothin in common and I have no clue on how my application will be evaluated.

I have strong letters of recommendation from Ph.D and from a former professor in computer science. My GRE score are Q:159, V:153, A:4. My GRE math subject is 720 (62%) and TOEFL is 105.

Since I am a permanent resident ( green card ), I can live in the US and do pretty much whatever I want. The issue is that I have no family here and I absolutely need some financial support to live. I know most Ph.D are fully funded and a handful of masters are. Here are a list of options available to me and I would like to have some advice of someone knowledgeable in the proess of application to tell me which option is the best to reach my goal.

I am really interested in the academic world and if given the chance would not come back to industry work.

1. Apply straight to Ph.D programs in pure maths ( with a logic track )
2. Apply to funded masters programs in pure maths ( with a logic track )
3. Apply to a computer science Ph.D or funded masters (with a logic track )
4. Apply as a non degree seeking student to some courses to build some convincing grades.

I only considered and taken actions towards option 1 at the moment ( applied to 6 schools ).Since I want to apply to one program in each school, I would like to know if I have any chance for the options listed above and which one is the fastest path for me to reach my goal. Is there any other options I haven't considered ?

Any member of a graduate committee here can help me ? Any graduate student familiar with this situation ? Or any insight is really helpful.

Thank you.