Sure, but the 4th and the 2nd aren’t playing simultaneously. If you listen to Baroque music, you’ll here suspensions that hang on the fourth, release and go to the 2nd, then resolve on the 3rd. This does something similar. It goes 2nd-4th (with 7th)-2nd-3rd.
When I encounter chord spelling problems like this, I think, well, what does the chord sound like in context? To me, it does not sound like a major chord, it certainly does not sound like a minor chord. It sounds like a suspension that is strongly leading to a resolution. I do hear Bb as the bass for the spelling of the chord, therefore, I’d like to call it some sort of Bb suspended chord resolving into a Bb7.
I mean, I see why you want to call it a ii-V-I turnaround–it’s just that when I hear it, it doesn’t sound like what you’re calling a ii chord is functionally acting like a ii chord. But things aren’t so clear-cut in harmony. The same chord can be notated many different ways, but Fm11/Bb looks bad to me.
And I’m not exactly sure why the fact the F would be a dorian chord is relevant to the spelling. The 11th of a chord notated as Fm11 chord is always Bb, whether dorian, phrygian, aeolian or whatnot. If I encounter an F7 chord in the key of C, the 7th is Eb, even though the F lydian 7th is an E natural.