Is there anywhere you can go and hunt elk in mid October?
You can in Idaho from the Oct 10th to Nov 3rd with the B tag or from the 25th to the 30th with the A tag and it is during the any weapon season and lots of rifles.
Kentucky -- if you can get drawn. Deadline for the draw is 4/30 and there will be 400 tags this year. Herd estimated at about 8,000 this year. There have been some big elk taken over the last couple of years.
Here's the link: Kentucky Elk Hunt Info (http://fw.ky.gov/elkapply08.asp)
You can apply online.
Lots of areas in Wyoming if you don't mind fighting the rifle guys. Non residents have to apply in Feb, however.
Montana's archery elk season goes into mid October - draw only for NRs.