Hi SINGLETRACK
I've done this route in total, and in sections, several times both at different times of year and in both directions. However, my times of year were between March & August (just happened that way) and not at the time you are planning. I see nothing wrong with September/October but campsites may well be closed if you were thinking of camping, and also the days will be shortening. My first trip was from Stornoway to Lochboisdale, mainly to fit in with ferry times, and of course I had to contend with the prevailing wind which on that trip wasn't too bad. Another ride was from Barra northwards and again the wind this time was coming from the north, whatsmore I had to contend with sleet and hail on North Uist, but it didn't last long and I took advantage of a peat stack for some sort of crude shelter. Midges? I've encounterd them on a non-cycling trip before but "NEVER" (yet) whilst cycling. That's one advantage of having a good breeze for much of the time. I clearly recall one year, June 21st longest day, I had just left Benbecula and was cycling south. The rain & wind came in and everything went horizontal - I made it to a bridge parapet for shelter and the thing was trembling. I survived.
I'm not sure if you've been before but I have loads of enroute photos. I think the whole route from end to end is only 140 miles depending on where you start & finish. Apart from the Harris to Lewis bit (na Hearradh a Eilean Leodhais) the terrain is quite flat if not windswept. I usually b&b and these have been in different places along the route. I have never stayed at the Howmore or the Lewis (the name escapes at the moment) hostels though so they might be worth sounding out as an overnight option.
I could rant on about this for ages but suffice to say "in the right weather conditions" this is one heck of a route. I hope to do many more in the future.
Good luck with your planning.