The best training you can do is the actual task at hand - that is walking all over the hills gaining and losing elevation with a heavy pack.
As far as the mental toughness aspect - its absolute BULLSHIT that it cannot be "trained". No one comes out of the womb "mentally tough", same way people don't come out of the womb killing elk or climbing mountains. To me, "mental toughness" boils down to optimism. If you get inside your own head because you haven't seen anything in days, well yeah of course you're gonna want to run down the mountain and go home to the wife/kids. The mental toughness aspect is remaining unwaveringly optimistic, even if you haven't heard or seen anything in days.
What helps it? For one, having a proven and comfortable sleep system. Seriously, more hunts have been broken because some macho guy figured he could hit the hills with nothing but a blanket and a 1/4" foam pad. Some guys can sleep like that - but most can't. Be honest with yourself about what you need and leave the machismo bullshit out of it. Need a pillow? Bring it. Need a soft cushy mattress? Bring it. The more rested you are the better your attitude will be.
Second thing is keeping well hydrated and fed. Climbing up and down mountains all day is absolutely draining, and I don't know about you, but elevation really makes me lose my appetite. If I let it go and deal with it at the end of the day, I'll bonk and its hard(but not impossible!) to come back after that. I force myself to eat every hour if I'm hiking. I don't restrict my fluid intake whatsoever. Another thing that helps is having food that actually tastes good. If you're truck camping, its no big deal. If you're camping off your back, invest in the decent meals like the Peak ones. Yes, I hate paying $10 for a meal... but it actually tastes good and makes me want to eat it. One thing that I've been doing while truck camping is waking up early enough to get a good breakfast in(doesn't necessarily have to be elaborate, just something filling), and making a "day bag" for myself that consists of something substantial for lunch, a ton of good snacks, and a zipfizz/liquid IV.
Don't be afraid to nap or break during the day. If you have an adequate time for hunting(say you took 2 weeks), don't be afraid to have a down day where you maybe hunt the morning/evening and rest the other part of the day. You can bring a fishing rod or something like that, that's always a welcome distraction when the action is slow. Go catch enough brookies for dinner - talk about a morale booster! Not a great idea if you're in a time crunch, but if you budgeted enough time its great. Don't forget to bring your weapon along - those damn animals like to show up at the damnedest times.
I find having a fire at the end of the evening a morale booster as well. Not so important in August when its balls hot out, but in September on when the evenings can get chilly. Bonus points if its a fire in a wood stove - nothing like coming back wet from sweat or rain and being able to get warm and dry your gear out for tomorrows hunt.
Finally, back to the original subject - being in shape. It helps a ton when you're not getting your ass kicked up and down the mountains all day. Whenever a 3k 10 mile day is "okay" and not an "ass whipping", its a hell of a lot easier to remain optimistic. I would be loading your pack up and walking uphill and downhill. Don't waste time "walking the neighborhood" as its hardly helpful. I guess it will help some with your straight line endurance, but know the mountains are rarely a straight line. If you don't have mountains nearby to hike, a step mill at the local gym will help... so will a treadmill set on max incline. Hell, even hitting the stairs in your house for 1k/2k "up" steps will help more than walking flat ground.
On the weighted pack - you should know how much your pack weighs with a day load out and a backpacking load out. If you plan on hunting primarily from the truck, get your day pack weight including snacks, lunch, water, weapon, etc... and then either purchase a water bag or bags of concrete and use it in lieu of your gear. No funny looks while you're out on trail, and I'm sure most gyms these days would probably kick you out/ban you for bringing a weapon inside... bonus - if your pack gets stolen out of your rig while you're out it won't have all your gear in it. Just make sure it weighs at least the same as what you intend on carrying.
I do not think you have much, if any, advantage with your line of work. I guess you have more than a cubicle dweller/desk jockey, but it isn't enough of an advantage to go into it without training unfortunately.