The tongue weight for an AS includes the LPG cylinders full, the battery bank, and the base trailer without options. Options include an additional battery, a more comfortable mattress, and camping gear, as well as the weight distribution hitch. The published tongue weight is also a dry weight without fresh, grey or black water. So do not rely on the published tongue weight to be the maximum you will have when ready to go camping. Investigate what folks have measured their trailers to weigh and estimate what you will add, what it will weigh and how it will balance. That will give you a better idea of your actual conditions.
See above comment to check axle and tire weights. Surprised that the limit is 500#s, but the models have changed. TV tongue weight capacity is calculated by the OEM engineers and considers the mass that is removed from the front axle by the applied tongue weight. That is why some rigs have more tongue weight capacity if Weight distribution is used. This is the key to your question and the answer you must determine. There are some other issues, including axle, tire, spring, and receiver capacity. Some factory receivers are only designed for a specific tongue weight. If that is the controlling parameter, an upgraded aftermarket hitch might serve you well. However, not if the axles will not support the load you want to carry. Check the axle ratings first. You can replace tires and wheels with heavier capacity components.
Next, there is the load you carry in the vehicle - people, drinks, pets, tools and camping gear that will not fit in the coach. The tow vehicle must handle that payload as well as the tongue weight of the trailer. Payload total includes tongue weight. They are not separate capacities.
You have a lot of figuring to do. The tongue weight needs to be at least 10% of the trailer weight to be stable. A total of 15% is considered ideal, but a very stable tow vehicle, lower travel speed and active driving likely offsets some of that requirement, maybe.
Driving speed has another effect. The Goodyear Marathon tires fitted as OEM standard are ST or specialty trailer tires. They have a significant load rating, but are limited to 65 mph. Above 65 mph the ST tires build heat which destroys them over not too long a period. The 65 mph limit is also associated with stability and tongue weight. Traveling slower is more stable. Research tires before you buy.
The two trailers you are considering both are good choices, but for very different reasons. Purchasing the trailer that can be towed by the existing tow vehicle is a consideration, however, a lot of folks tend to trade up over time. If you can find the layout that really works for your lifestyle, you can maximize the trailer investment by keeping it longer. Be careful with your choice.
Also, you can do a lot of modification to a paid for tow vehicle. That might be an option to consider. Alternatively, if you are not a DIY mechanic, trading up for a lease return with a good warranty might move your RV plan forward. Investigate and make your plan. A wise man once told me that there are a lot of ways to make an idea work. Some might even be yours.
Good luck with your investigation. Make it happen and enjoy the adventure.