Have you considered a elk hunt in canada? Alberta, Sask ?? There are a couple options. You can pay for a guided hunt or have a resident hunter host you...under a hunter host licence you can hunt for the cost of the tag and licence fees ( under 400$ CDN) as the hunter host cannot take payment...not certain about getting meat back state side but I'm certain its possible. Anyways with the cdn dollar how it is right now it's probably much cheaper than a out of state hunt...https://albertaregulations.ca/huntingregs/licencecosts.html#:~:text=Prior%20to%20purchasing%20any%20licence,Wildlife%20Certificate%2C%20which%20costs%20%2468.22.
You would be looking at non resident alien for costs... then you just have to find a hunter host... or look for a guided elk hunt.
Just giving you an outside the box idea.