I have a similar situation, given that I have access to 2 403bs, 2 457s, 2 IRAs, and 2 HSAs between my wife and I. We actually have more tax advantage room that we do income (I know, what a terrible problem, but if it makes you feel better there are no matches)
IF your plan is to retire early, you should be maxing out tax advantage space as much as possible. You can get to the 457 as soon as you retire and there are multiple ways to access your 403b money early as well (search forum or internet for 72t or roth pipeline)
My plan has been this:
1. Max out HSAs
2. Max out 457s
3. Dump money into 403bs until tax due is zero
4. put money into Roth IRA
If we made enough money, we would still max out all of these before we moved over to taxable investing, so in your shoes, I would still look to ram and jam as much as possible into the 403b.
Good luck!