I'm not doing this now, but have in the past. (Now I focuse more on the mountain training but still try to run consistently.)
I was surprised at the degree to which mountain ultra fitness was not ideal for hunting fitness. Back in 2016, I trained and ran decently well at a 60k with 10K+ of vertical gain but was still pretty bushed for hunting, mostly due to the off-trail nature of hunting, lack of mobility, and lack of "accessory strength" such as grip strength and carrying heavy loads. Basically, I had gotten quite good and chugging up- and downhill at moderate-to-fast speeds, in a straight line, on a trail. But I got pretty fatigued and sore during and after the off-trail hiking, skinning, and carrying heavy loads. At that time, I peaked at around 60 mountain miles a week with some bodyweight strength training and some mobility work. I think I had 6ish long runs of 20 miles or more. I did one workout run a week, starting with mile repeats and then doing hilly tempo runs, long run on Friday, easy runs in between. I did three ultra races, a trail marathon, handful of ultra-length "adventure runs" on basically that same routine.
Now I feel much better in the hunting context. Hard to get an objective measure of mountain fitness, but I did a guided hunt last year, stayed up with the 19-year-old sheep guide, no soreness, felt great even skinning things out and carrying heavy packs. Have been following an Uphill Athlete guided training plan involving 8-week blocks of aerobic base, strength, and muscular endurance. Trail mileage of 30-40 miles a week, mostly running, two strength training sessions a week with more emphasis on higher weight and lower reps, dedicated blocks of loaded pack carries on steep terrain. I don't really do long runs any more, mostly due to time constraints, or could be laziness. I get my 30-40 miles a week with 7ish mile runs, mostly on trails.
I'm probably going to take a crack at some longer ultras next year, but will maintain the strength training and muscular endurance components. I think they add a lot and I certainly feel better with them in the mix.
For you, I'd suggest supplementing your running mileage with 1) consistent strength training...can be very simple such as choosing three main lifts to focus on and doing them 2x/week; and 2) perhaps one 6- or 8-week block of heavy pack carries on steep terrain. If your base mileage is high enough, it should provide a good basis to support some hunting-specific fitness as well.