You are correct. We can't really infer much about Una's citizenship status and so letters of recommendation or sponsorships aren't of concern. But with that being said - if Una can be a citizen and be modified then so could Dal. Albeit the restriction on genetically modified people serving in Starfleet seems to stick all the way through to the late 2370s and early 2380s at least.
In fact, unfortunately, we still see a fair amount of bigotry towards modified people persisting into the 2370s, but perhaps by then the difference between a modified Ilyrian and a modified human are more substantial. Dal, being a non-human (I guess?) might face less bigotry in his era than Una faced in hers.
To your comments about the floating nacelles - what's even supposed to be the point? I can't imagine how having nacelles detached offers that much of an advantage.