I have about 20 weeks of hauling 35C batteries in my future. A total of roughly 750 batteries at 25lbs each all over the great state of Arkansas. My question is, if I load my trailer to axle capacity will I still be able to use the payload (lbs) of my LR4? Or are these two entangled? Also, if anyone can speak to gas performance of full payload that would be of help as well. Thanks in advance!
Why do you make other people do the math?

It's easier to help if you present all the specifics.
Anyway, 750 x 25 lbs batteries only weighs 3200 lbs. What does your trailer weigh and is it a tandem? I wouldn't use a single unless it was a light open flat bed. Still I'd prefer a tandem with 7000 lb gross weight and a 2-5/16 ball. A brake controller is important for that weight level.
To answer the question about cargo, you have to be very mindful of what is on the vehicle, including the hitch. You cannot max out the cargo load if also near the limits of the trailer and tongue weights.
The LR4 will do it just fine. It's engine, transmission and brakes are better than my lr3 and it does more than that without too much drama unless I'm trying to pass slower vehicles.
The other thing is you have to be clear about your lr4 base weight if there are any added parts or gear. Most people with fully kitted vehicles are already at the GVWR before towing anything at all so tongue weight and/or cargo are more critical.
Gas MPG? That's funny. It will suck. 13 on my last trip towing 250 miles a tandem 6x12 low rider not loaded too crazy. It's the wind that matters the most on the highway.