The support engineering role can vary from organization to organization. In a support role, you probably won't grow all your coding skills as fast as if you worked full-time developing. You will get good at debugging and some other aspects of development, but you will likely build less and grow less in some areas (unless you spend time during or outside work building). You will still grow, though.

These roles can pay less, it depends. Your market rate is largely a function of interviewing skill and negotiating skill. Work on both of those. Keep interviewing and find the right fit somewhere. Sell yourself (technical and non-technical skills). Did you lead a team at your previous company? What value can you add to projects in your potential new job?

Ask 3 at interviews - "How many support engineers in the past year now work 75%+ time building software for people, internal or external?" If there are previous support engineers, that will give you insight.

Keep practicing your interviewing. You may need to learn some node and a latest (e.g. React, Angular) front-end library. One way to demonstrate is by building a small project, hosted on GitHub, which shows you can build software. These two things (especially interviewing better) is very likely the only thing between you and the job you want (full-time software engineer).

Ways to interview better include practicing white boarding by doing algorithm problems. Think out loud during that, and ask clarifying questions. Same with onsite coding- think out loud, ask clarifying questions.

You have cs degree from a top school, and some entrepreneurial experience. These have value. Many roles are open to you- find one that's a good fit for your and your employer's sake.

Referrals will help you, too. Having an advocate inside the company who knows you will make it more likely to give you a chance.

Good luck!