I think that the 'residency' term is misleading. All it really means is a prolonged 'new grad' orientation, regardless of where you work. It's all semantics. For instance, I might work at a hospital with a 'residency' and get four months of new grad orientation, and you might work at a hospital without a formal residency and get four months of new grad orientation. Even though mine is called a 'residency' and yours isn't, we're still getting the same training.
It seems to me like the real issue is getting hired as a 'new grad' in your area with an ADN. From your post, it sounds like your local hospitals are willing to hire experienced ADNs, but not new grad ADNs. You're in a unique category as a former LPN with a decade of experience; you bring pertinent nursing experience to the table but you're not an 'experienced ADN.'
Do the hospitals with new grad postings say 'BSN preferred' or 'BSN required'? If preferred, I'd definitely submit your application. Even if it says required, it might not hurt to submit your application anyway. Given your work history, you may be a stronger candidate than a new grad BSN without any work experience. I'd cast a wide net; apply as many places as possible, and don't shy away from facilities just because their new grad onboarding program doesn't include the word residency. It's totally possible for 'non-residency' units to have an awesome new grad orientation, and for programs that call themselves a 'residency' to have a terrible new grad orientation.
If you can't get a hospital job right out of school, still try to use your ADN. You say that you might stick with what you know; unclear if that means your employer, or specifically your LPN job. Even if you stay with your current employer, I'd definitely work under your ADN license rather than staying in your LPN role. That way, if you do decide to apply to hospital jobs later on you'll be in the 'experienced ADN' category. Once you start in the hospital, you should still receive an extensive, thorough orientation adjusted to meet your needs and level of experience.