In New Mexico you do not have to shoot a full bore projectile (like the Thor bullet), so you would likely save headaches by shooting a bullet in a sabot since the barrel is likely cut with rifling optimized for a sabot. If you like what you read about Thor Bullets you can shoot saboted Barnes bullets in sabots for similar performance.
If I had an Umtimate Muzzleloader, and was hunting New Mexico (minimal muzzleloader restrictions) I would be wanting to take full advantage of the high BC (ballistic coefficient) bullets available for muzzleloaders in sabots to really get the most range out of your rifle. Take a look at Parker Productions bullets:
http://www.parkerproductionsinc.com
From what I understand, the Remington Ultimate Muzzleloader is a recent rifle that comes off of the "Ultimate Muzzleloader" patents. Look on the internet look for links to Ultimate Muzzleloader since there will be more history on this rifle than the newer Remington offshoot. Here is a link to the Ultimate Muzzleloader website. On there website are some bullets they recommend for their set-up:
http://ultimatefirearms.com
It's also my understanding that "Ultimate Muzzleloaders" are designed to shoot pelletized 777. I far prefer loose powder for accuracy (like BH209) in my Knight muzzleloaders, but that may not be recommended for your muzzleloader. A friend with an Ultimate Muzzleloader tried BH209 had to send it back to the factory to deal with some damage to the rifle (breech plug I recall). If the rifle is designed to shoot BH209 powder that would be my preference.
Always hunt on a fouled barrel, unless you prove first shot out of a cleaned rifle tracks the following shots well.
Track down some of the Ultimate Muzzleloader videos on YouTube for the loads they recommend. I know I have seen some in the past. I'll do a quick search on YouTube for "Ultimate Muzzleloader" and see what I find:
Ultimate Muzzleloader:
https://www.youtube.com/watch?v=Qq9GGU5k9X8
Ultimate Muzzleloader:
https://www.youtube.com/watch?v=PvgmWUHWgtk
Remington Ultimate:
https://www.youtube.com/watch?v=-lPaB2w2uNA
Remington Ultimate:
https://www.youtube.com/watch?v=jbAsgJHHuzw
There are a lot more under that search.
Before trying the hot loads shown in some of these videos verify what the allowable amount of powder is with your particular muzzleloader!!!!
