From what I can tell, the 27 year limit also applies to the “non-scholarship” college program midshipmen. However, I recommend that you directly email (or phone) a NROTC unit. Recommend addressing your correspondence to the Executive Officer (called “XO”). He or she can, and will, answer any questions you have.
Looks to me like the Marines would take you in their Platoon Leaders Class. They give an extra year, 28, for graduation/commissioning. You train with the Marines during the summer, with no activity during the school year.
Personally, if I was in your situation, I would simply enlist in the Navy (or other service) and see if you could get the military to pay for your education. Generally the age limit that way is 30 or sometimes higher.
Good luck.