First, the "perception" of "Stabilizer" jacks is really completely wrong. Those jacks are really designed for one purpose, and that is to keep the trailer from tipping if too much weight is placed on the end, and really, that's about the only real expectation out of them.
To use to stop trailer shake is near impossible. The only way to make that happen is to get the trailer frame on something solid and the wheels completely off the ground.
There are some things you can do to help eliminate some of the "shake" with your current jacks however. But it will not eliminate all of it. By nature and design of the jacks, the way they are attached to the camper frame, you'll never have a "rock solid" feel inside the camper if this is the only device you are using.
First, make sure you have something solid under the jacks on the ground. Many use Lynx blocks. Personally, I don't like them. If parking on grass, sand or dirt, the first one will sink into the ground because of the hallow inside of the block. Once it's completely sunk,it may work pretty good, but then, you'll need to continue to tighten your jacks until the bottom one is completely squished in the ground.
Lumber (in my opinion) is a much better solution. Although lumber is heavy, and harder to store, (in my opinion) stabilizes more sound than the Lynx blocks. And the larger the board, the bigger the foot print on the ground, the less the board will sink into the ground, grass, dirt.
Another factor that makes the jacks so inadequate by their design, is simply, the longer they are extended, the less stable they are. So another tip is to build up a solid base under the jack as high as possible to the bottom of the back, before extending the jack. Shorter shaft on something solid makes less shake in the camper.
Next, if you are using electric jacks, does your electric system have enough "umph" to actually lift the camper? If not, it's possible the electric motor does not have enough "umph" to put enough pressure on the jacks to make them stout enough to help prevent shake. Hand tightening, that extra turn, that extra "umph" can make all the difference in the world.
A few winters ago, I parked my (previous) camper on grass at home. I had 6 jacks, plus the tongue jack permanently attached to the trailer. All 6 were down on lumber. I also had 4 manual bottle neck type aluminum jack stands I placed between the jacks attached to the trailer. They also were on lumber, and I'm talking 2x6x24 inch or longer boards under each jack. I also also shortened the distance from the ground to the bottom each jack by adding more lumber. And guess what? even after all that, the trailer still had wiggle to it. By spring, when the ground settled under each one of those 'pads' on the ground, there was enough wiggle and shake back in the camper, it was as if the jacks were not down at all. They sunk in the ground that much, and I did not keep them tight through the winter and spring when the ground started to thaw.
Unless your stick and brick house is built on a concrete slab, even someone walking across a wood floor will cause vibrations across the floor, and sometimes can be felt in another room of the house. When we were house shopping many years ago, we were shocked how shaky second floors were in stick and brick houses, by simply slamming a door in one room, you could feel the whole house shake in another room. I'd hate to think what the washing machine and dryer would do?
That's why we ended up buying a house built in the 1950's, that was still built with real wood and real construction methods. That taught me a lot about stabilizing a travel trailer too.
You're going to have trailer shake, no matter how hard you try to eliminate it. When it does shake, just enjoy the moment and be glad you're in the camper and not spending the day at work! It will put a smile on your face. ... guarantee it!