I think your math is incorrect. And I'm guessing you aren't using a WDH...or at least not correctly, because of the unloading of the front axle on the tow vehicle.
Generally speaking...and in most cases...
Dry hitch weight includes the weight of the empty propane tank(s). It does NOT inlude the weight of battery(ies) and propane in the tank(s).
Published hitch weight: 413#
Battery weight: ~60# x 2 = 120#
Propane weight: ~20# x 2 = 40#
Theoretical tongue weight without ANY cargo: ~613#
With no other items packed in your rig, your tongue weight will be much closer to 613#. These things don't move well, so that's your starting point. Those items are NOT on the hitch ball, so the axle carries a tiny fraction of their weight...but 613# is close enough for guesswork.
When you add cargo to the rig - clothes, cooking utensils, dishes (even paper plates), towels, toiletries, and so on, placement in the rig adds to or subtracts from tongue weight.
You understand the 10+% rule for tongue weight as loaded.
This is the 2024 version of the rig. The numbers seem similar. Looking at used listings, the floor plan seems to be pretty much unchanged. So I'll work from the 2024 factory specs.
Risks:
1) Giant passthrough storage under the bed to accumulate lots of weight well forward.
2) Giant pantry/wardrobe between the kitchen and the bed...can also accumulate lots of weight.
3) Your hot water heater is likely full. 6 gallons at 8.3#/gallon well forward of the rig's axle = 50#. So, even if you don't fill your fresh tank, you're carrying water unless you drain the hot water heater each time you hit the road.
Reverse Risks:
1) That fridge and the bathroom can hold lots of stuff = weight.
You missed a step in your weighing routine. Echoing others, what you need to do is load the rig for travel. No fresh water, since you don't need it. Take it to a CAT scale and weigh the tongue and WDH -- OFF THE HITCH BALL...just the tongue jack and WDH on the scale. That tells you what's crushing down on the bumper pull hitch receiver on your tow vehicle and eating into your TV's payload capacity. The CAT scale will tell you facts...not conjecture.
Next, remove the WDH from the CAT scale and get the actual tongue weight of the rig so you can calculate the safe % that should be on the hitch ball for stable towing.
If your tongue weight is too high...above 15% and well above what your tow vehicle (TV) can handle (with the roughly 60# WDH bearing down on the receiver), you can adjust your loading tactics to move some heavy items to the rear of the rig...say in the shower...to tweak the tongue weight. Just be sure to maintain an absolute minimum of 10% on the tongue...12% would be safer. 532 pounds (without the WDH) would be a good target.
Bear in mind that if you remove 1# from up front and move it far back, the net result will be a nearly 2# change in tongue weight. That 1# in the shower will apply about .75# of 'LIFT' on your tongue...just as the current configuration UNLOADED the front axle on your TV. Moving a pound from the pass-through to the shower has nearly double the impact on tongue weight (based on where the rig's axle is located).
Then weigh the entire rig, including rig's axle and the tongue jack on the scale, WITHOUT the WDH to get the actual GVW (4437 allowed on the 2024 model) and see if you are overloaded or not. The specs say you only have 894 pounds of cargo capacity. You've used 200# of it with batteries and propane. If your water heater is wet, that's another 50#. 644 pounds of cargo doesn't go far. You'll be surprised. And if you were to add 31 gallons of freshwater (minus the 6 gallons of rated capacity that's actually in the water heater) at 8.3#/gallon, that consumes 207# of the remaining 644...leaving you with just 437 pounds of cargo. It goes fast. BUT IF YOU COME IN SIGNIFICANTLY BELOW GVWR, you might lower the tongue weight by a smidge by moving load behind the trailer axle. Just do the math for 12% tongue weight.
Keep track of the loading tactics that give you a safe tongue weight, so you can repeat them.
If this rental is a test drive to see if you like RVing, learn what you can about your RVing habits so you can make an intelligent purchase later. By all acounts, this rig is intended for boondocking (thus the two batteries), so traveling wet will be part of the deal if used as intended. If you are into RV parks with hookups, there are far better choices that your TV can tow - preferably with two axles.
Repeating...I think your math was wrong...or too much of the cargo in your rig is forward of the rig's axle. The CAT scale will tell you the facts and educate you on how best to load any particular RV. It seems that you found a CAT scale, you just need to adjust your tactics a bit so you can correctly load your rig. And if you don't have a WDH, either get one or rent one with the rig.
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