Oh. Nevermind. The person said he thinks gaps are okay as long as it doesn't mean you don't meet the 2 years. Like...1 year 10 months and then we went away because my visa expired. As long as we did cohabitant for 2 years straight.
To be honest, it's a little bit of a grey area, because I think technically, you should have been living together for the 24 consecutive months immediately before applying. However, I think there may be some leeway if you had lived together for at least 2 years before you had to return to the US.
As you said, if you had only been living together for 1 year and 10 months and needed those last 2 months (August and September) to meet the 2-year requirement, the visa would likely be refused, because you were not living together in those 2 months and therefore would not have lived together for 2 years in total.
But as you lived together for more than 2 years before you left the UK, and the only reason for living apart was your visa expiring and not meeting the financial requirements right away, then you may be okay.
Ultimately, though, your main concern at the moment is getting the incorrect visa and 'no work' issue sorted out... it may be as simple as just sending your passport back to them and them sending a correction and issuing a BRP. Right now, UKVI are the ones who have make the mistake, not you, so it's their error to sort out.