I think the objective goal is to get the same amount of weight to be added to both the front and rear axles.

In reality, that's probably not realistic, nor is it what the car designers would expect. I mean, if you just load up the back of the truck with cargo (no trailer), the weight goes on the rear axle, with no additional weight on the front.

So, find a reasonable compromise. When you are done, the handling should be "confident," and the trailer should be level.

If you can't get there, you might have just a bit too much tongue weight.