The real problem is most outfitters are booking 2025 or later. A guided elk in CO will be easily likely $6000 or more. I would start visiting outdoor shows. There is the Springfield, MA show that will have lots of oufitters but granddaddy of them all is the Great American Show in Harrisburg, PA. This show is nuts! If you think you are going there, book a room NOW. Look at the outfitter lists for these shows, start researching what you want to hunt, where, when and possibly with whom. Research State guide license certifications for actual license and any complaints and resolutions. Complaints are not necessarily outfitters fault. Clients have responsibility as well and some don't want to shoulder their own failures.
The drive from upstate like Albany is not too bad. Plan on at least 12-16 hour day drives. One hack we have done is stay at KOA Kabins. You can reserve them so you have a destination for each night. Good security since you are parking next to Kabin and have good CLEAN shower facilities. Pairing up with 1-2 makes the trip easier and adds to the adventure and experience.
Lots of threads here on LRH for transporting meat. Lots of threads on physical prepping, altitude prep. Western trips from NY are road trips within themselves.
Another option is opposite direction to Newfoundland for combo moose, caribou and or even black bear. I have NY friends that do that instead.
