Can you do all three? Looking for jobs is not full time. You look for jobs, apply, and when there is an interview, you go
Subbing is also flexible, you can work whenever you want. In the meanwhile you can focus on your thesis.
Don't think of it as not looking for a job, it's kind of a waste not applying for a job, because you want to focus on your thesis. I did my thesis during student teaching, and was able to do it without getting stressed out.
There is a big chance you might end up subbing for a year or 2, (although you might get a job right away, but you won't know unless you apply), so it helps not to expect to work as a teacher right away.
I've been subbing for 2 years, and I haven't really applied for any jobs up until now. I think this was partially because I didn't have any experience, and I knew if I was up against teachers with 5-10 years of teaching, I wouldn't even have a chance, so I didn't even try. And I was working at the lock ups all this time and I've really enjoyed it (and I was in a LTS for 8 months). But now I realize that I want to work specifically with at-risk students, and I feel that I have enough experience (2 years) so I'm going for any job I see, that is working with at-risk kids. And I feel that I have a better chance.
Subbing gives you experience, but you might also learn about your preferences more.