You are say you are planning, do you have any particular detailed route plans I could critique? To a first approximation, my guess is that this is unrealistic in conception, mainly, but not only, because of the dates.
Hut to hut mountain biking suggests the interior, and it is risky going to the interior on a bicycle that late in the year, at least very far into the interior. I think you'll have to take a tent even if the huts are present on the ground, because a lot of the huts will be locked up already at those dates. Also I'm not sure where you'll find a route you can reliably get from hut to hut in a day. Clearly there are some possibilities, like riding the Laugavegur footpath, which these dates are generally too late for, and the huts will probably be locked up, even if the passes aren't completely snowed in yet.
There is very little single track in Iceland. The reason is that few footpaths are sufficiently well walked to be beaten underfoot even for walkers, let alone cyclists. Paths like Laugavegur are the exception. But probably a guide will find you some, though you'd make it a lot easier for your guide if you came at sensible dates when he could take you along Laugavegur. You'll also find Iceland has a lot of very loose ground and riding a bicycle on anything which is not a very well beaten track or path is difficult because of the looseness of the material under wheel.
The problem with going to the interior at these dates is knowing when is the big snowfall that closes lots of interior roads is going to come. Some years it has already come by 17 Sept, though probably around about last week in Sept is more common, and it can be delayed until well into October if you are lucky. But suppose it hasn't come yet. Probably some of the very remotest/highest bits are already closed at this date (and high bits like the passes on the Laugavegur path), but probably quite a lot will still be open. Nevertheless between 17 and 28 Sept you'd expect a fair bit more, possibly a lot more, to close. So you'd have to keep a close eye on the weather forecast, with equipment to ensure you can do that, and at the first sign of a bad forecast get the hell out of there. And on a bicycle you may be too far in to get out in time, because the buses won't be running to rescue you, and there will be little passing traffic at those dates either. Possibly if you have a guide with a 4wd who can drive you out when the bad forecast is showing, that would work, but it would be very expensive to have that high level of support service.
For most cyclists, the 4wd tracks are quite hard enough cycling. Many of the 4wd tracks are as hard as single track in other places, hard enough to include some pushing.
I think you could try some of the more peripheral tracks at this date, without too much risk of getting snowed in, in the sense of having enough time to get out of there when the bad forecast was showing. But I think you'd probably need a tent. Or maybe you can plan it so you can stay in some guesthouses, if you are the very fit cyclist you say you are. I'd look at some roads like the ones going along the S & W side of Langjokull. You could risk a ride into Landmannalaugar, if it's still open, having had a close look at the weather forecast first, but probably you'd have to take the main tracks, the really excellent minor tracks in the southern highlands go very high and close early. And the hut will almost certainly be locked up at that date. They don't have a definite closing date, and can stay open a week or so into Sept if the weather is OK, but not in general very much longer. Then there is the issue of where you will stay on the approaches, you'd have to be strong not to need that.
