Funny you should ask
I having just retired my Subaru Outback from towing after 6 years due to the issues of the limited tongue weight
limit so I can relate to your problems. *BUT* I was towing a 16' with it and had to run with it at about 40lbs over the tongue limit to get a stable tow but that was due to its heavier axle weight than your 13'. I would think you would have little problem getting 10% or more on the tongue of your 13' without adding water to the rear & still stay under 200lbs. I loved how well the Outback towed so I think with a 13' once you get it set up right you should not have to fuss or worried much with it at all.
First I would not add water to the rear to fix the problem. Water or anything else at the very rear with a tongue that is on the light
side to start with is not a good thing - trust me on that!
sway is not a nice feeling! Yes you can add an anti sway bar but it will be called to use way more than it should be - should only be needed in extreme situations. Just in case no one has told you the best way to stop sway yet - there is a lever on your brake controller that you use. Do not use the brakes
on the car. If the trailer starts to sway just use the controllers lever never the cars brakes
Have you weighed the trailers tongue with the trailer *sitting level* to see how far over you actually are? Put a level not only on the tongue but at mid point on the trailer body itself - you may find there is a little bit of a difference. I would think that a 13' Scamp even with the shower up front isnt going to weigh anymore than 1500/1600lbs loaded on the axle (based on looking at the real world trailer weights thread) which means if your tongue weight at say 160lbs would be at 10% or slightly more which should give you due to the wheel base on the Outback a good solid tow. There should be no need to go over the 200lb limit on the tongue unless you have things other than the propane
tank and battery
that are really heavy stowed at the very front of the trailer. I know your manual says you can go as low as 8% on the tongue but personally I tried that and it wasnt good if you plan on driving at over 55 mph - that number may work ok with a boat but not a TT. I would rather not have to count so highly on a sway bar to keep me out of trouble. Personally think 10% or higher is better. Depending on what hitch manufacture/style you are using you may find you need to use a drop receiver on the tug to get the trailer level - I have to use a 2' drop receiver on my Outback with the current hitch that is on it - the first hitch I used only had a 1" drop receiver.
Even though I have drop receiver on the car nothing has ever hit the ground or come overly close to hitting the ground - even over big speed bumps at speed, so I am a little puzzled a to why your 13' would be having such issues. I know that the 13' do sit a bit lower to start with than a 16' but due to my trailers age I do know the axle has sagged a little so would not think it that much higher than a 13'. The rear of your Outback is higher so the hitch sits much higher than on a Legacy so it doesn't make sense to me that the tongue should be coming close to bottoming out. Unless you have the trailer with the nose to far down, which would also account for why it may be over 200lbs on the tongue as well.
Rather than putting weight at the extreme rear its way better if you add some weight closer to trailers axle - just over it or behind it if your to heavy on the tongue. Try moving things around a little bit inside the trailer. If you have everything stored in the front hatches and not much in the middle or rear that can be a problem. How I dealt with changing tongue weights due to my propane
tanks state changes or occasionally having to drive a short distances with water in the rear tanks when going dry camping
was to use a large rubbermaid tote that contained all my power cords, power adaptors, blocks, hoses, jacks, etc. It all adds up weight wise. Put it in the trailer in the middle of the kitchen when traveling - move it back or forward depending on the state of tongue weight. If I had water in the rear tanks the box was always moved forward of the axle. If no water in the rear the box sits right over the axle. Depending on where your hot water tank is located in your 13 adding water to it if its just a bit behind the axle may also take some weight off the tongue if your really have to but due to it being close to the axle its not going to have the same negative impact of having the weight at the extreme rear.
If you are still struggling with it post a picture of your set up with the car and trailer sitting on a flat road as others may have some further suggestions as to how to correct your problem.