BUT With a young child and spouse in UK, the ECO will most assuredly check for NHS debts!
They will. Gone are the days of having NHS debt and still getting a visa. When this change first came in to stop people entering the UK when they had NHS debt, it was 1k+ debt and then reduced to £500+ at a later date. Even in the UK, NHS debt owed is chased through the courts and if they aren't in the UK, their sponsor pays their debt.
But this can be recovered from because you did not use deception in your application. That's a massive plus.
If you had denied using the NHS and got caught out, you would have received a 10 year ban to the UK for deception.
The news rules in January also brought in a 10 year ban
from the UK and although that likely came in because of those in the UK under EU rules and Brexit, it will also affect those under UK immigration rules too who are caught out.
Even with British citizenship, if they later find out you used decpeption to get a visa to the UK, even if you didn't use that visa to as part of your citizenship application, they can remove British citizenship leaving that person with no lawful status in the UK. They don't get their ILR back.
You can see that what you have done can be sorted. An overstayer can stilll return home and get a UK spouse visa, but not if they have used the NHS and haven't paid; worked illegally; used false documents etc
Did you buy health insurance for when you were out of the US? If you did, get them to pay your medical debt. If you didn't, it could have been worse as you might have needed urgent lifesaving care that left you with tens of thousands, or even hundreds of thousands of medical debt to pay.