Ditto MT, not OTC, but has been a 100% draw lately. I'd suggest looking hard at some of the Block Management Areas in the eastern part of the state. It is a later season, so if you are in a tent, make sure you have heat, may not need it, but have seen snow and below zero stuff in early Nov more than once. I usually use a motel. 140's+ doable, but not a sure deal. I'd suggest looking for height and forks, before width, plenty of great bucks at or inside the ears. Spiking out overnight is probably not necessary on a BMA or in some cases possible (depending on ranch rules). There are tracts of public in MT you can find if you want to wander and camp overnight, but for a first time, I'd look to a BMA where I can get reservations to limit hunter numbers.
There are other options, but with what you have shared, it suggests a BMA in MT to me would be among the top choices. That said, if where you hunted elk has a decent deer population near by with available tags, that may make sense too as you have some familiarity with the area. There are places from OR to SD to NM and many points in-between where you can go with your trophy expectations and get a tag. Whatever you decide, I'd suggest picking a spot where you can hunt at least every other year for several hunts, in the event you like and want to repeat the experience. A key to getting better bucks is familiarity with an area. If you have a fairly flexible budget, buying landowner tags in other states, like CO, may be the ticket. Good luck!