It really depends on the bike, how you pack it for weight distribution, how heavy it is, how stiff your rack is, how high or low your panniers attach to the rack, how far back or forward you have your panniers mounted, etc.
The best way to find out is to load it all up with two panniers and try it with a rear load. If you do that, you could add a 10 pound brick to simulate a couple days of food on top. That is exactly what I did about six years ago, I was going to do a single track trip, my bike frame could be fitted with a 100mm suspension fork so I wanted to see how it handled with suspension fork on front and no front panniers. Used a 10 pound brick on top of the rear rack (the brick was in the paper bag to avoid scratching the rack) to simulate food weight.
I also added a really cheap frame bag to my frame, but only had a couple liters of water in the frame bag.
The panniers in the above photo are Carradry, very large that I bought specifically for that trip. (I usually use Ortlieb rollers.) For a variety of reasons, the trip did not happen, so I do not have an after-trip report. But I was not using a LHT, so there is no comparison here.
You did not say what your rear panniers are. If they are Ortlieb Backrollers, there is a strap that goes over the top of each rear pannier, those two straps can instead be used to attach the Rack Pack to the bike. I can add a photo if you would like.
Regarding packing, I always try to pack my weight as low as I can. A tent is pretty dense, I pack that in a pannier, I put less dense stuff up high, my sleeping bag is not very dense so that always is in the top of a pannier.
The exception to my rule for weight distribution is that when I come out of a grocery store, the groceries always go in the bag on top of the rear rack instead of unloading my panniers in a grocery store parking lot. I will fix any weight distribution (like canned food) the next morning when I pack up the panniers and the canned chili goes in the bottom of a pannier.