Adding more weight is not a good solution as it ADDS weight. Anything that doesn't go on the pin will only increase the axle weights. Weights behind the axles will add not only the weight of the item but also, whatever it takes off the pin weight (further back, the more it shifts weight from the pin to the axles).
You need to SHIFT existing weight towards the front (even if it's still behind the axles further forward helps). Is there gear in the garage you can shift to the front underbelly? Depending on the exact distances moved, it can have the effect of moving more than 100% of that weight off the axles.
Removing weight can help but again, removing it from further back is more effective. That's a big water tank. If it's over the axles, try running with only enough for a roadside potty stop and fill up when you get to your destination. 3/4 of a 115gal tank is 700lb on the axles. Likewise, can you fill the fuel tank at your destination? 30 gal behind the axles add somewhere around 400lb to the axles.
What you are seeing is a simple teeter tatter effect. If you have a 100lb kid sitting on one end and it's all the way on the ground, almost all the kids weight is sitting on end of the board with almost none on the center support. If you put a 100lb kid on the other end and balance, so the board is level and neither kid's feet are touching the ground, adding the 2nd 100lb kid added around 200lb to the center support.
Somewhat odd is toy haulers typically have HIGH empty pin weights so that when you load the garage, the pin weight is still in the 20-25% range. According to the link you provided, the empty pin weight starts at only 19%, so loading up the garage. Before you add the side by side, you are already down below 18%. I would expect another 1500lb in the rear will put you at a very marginal 15%.