transition from proprietaary market maker to bank trading?

I was wondering if anyone has advice for how to go from a proprietary market making firm to bank trading?

I have a strong academic background, although not from a target school ( i studied electrical engineering at university of illinois which is top 3 for that field, and I have a good gpa). After I graduated, I decided to take a job with one of the top market making firms in Chicago. I figured that I would do less of the clerical work and more trading sooner. This turned out to be true, and I've gained a lot of valuable experience from doing it. I ended up trading european and US fixed income for 2 years. I traded mostly futures but a few swaps as well.

What I've come to realize is that fixed income at a market making firm is a very limited view of fixed income as a whole. I'm not seeing any of the swaps flow, muni's, agency's, CDS, etc. Although I've learned a lot, I've come to regret not going to a bank's S&T desk. My question now is how do I go about doing that? I know I'd be most likely taking a significant pay cut, but I'm willing to sacrifice short term gains for long term knowledge. Unfortunately, my school doesn't place many people in banks in a trading capacity. I know a few salespeople that I've traded with, but I'm concerned that asking them would jeopardize my current job.

I've looked for jobs on banks career websites, but for experienced hires almost all trading roles need Series 7 licensing which apparently you can only get if you work for a member of finra. Should I apply as an analyst? Do they even accept experienced traders as new analysts? Is there anyway I can come in as a 2nd year analyst or associate or something that reflects having been traded block size on the exchanges(some of which I know was on the other end of swaps desks at GS, JP , etc?)

Any advice would be greatly appreciated. Thanks