The easiest one that comes to mind is clematis terniflora since it blooms in late summmer/early fall for people in most zones. I am sure that there are other large flowering hybrids that would probably bloom for you in the fall but the number of LFH I have in my garden is rather limited. I can get rebloom on some of them in the fall but this is accomplished by pruning them back in midsummer and keeping them watered and fertilized and they rebloom in the fall. In your zone, I am unsure if you can get this to happen since I don't know how long your growing season is.

I am going to defer to others in your growing zone or in close proximity to where you live since when a clematis flowers is going to be dictated a lot by your local weather and the specific type of LFH. Perhaps others in your area will have some specific varieties to suggest. Another idea would be to stop and ask any people in your area that having clematis blooming at this time the names of their clematis. This would help better insure that your bloom times would coincide with theirs for the same variety of clematis.

I don't think there is a fall-blooming LFH. The best you can do is aim for a second bloom by doing as Miguel says, cutting some type 3's back after their first flush is done. I've had success this way (and have blooms currently on) Ville de Lyon, Viola, Hagley Hybrid and Solina, though others may work as well.

michaelinchicago ... would love it if my villedelyon would rebloom! ... how far do you cut it back after the 1st bloom? ... mine is all brown & yucky-looking ... thanks, phyl

I have several small flowered varieties that bloom late for me, but no large flowered ones. I have serratifolia, virginiana, sweet autumn clematis, akaboides, Rooguchi, rehderiana, Bill Mckenzie, and Kerminsina that all bloom August-October. The only large flowered variety that I have still blooming is John Paul II. That has been blooming since May though.