The "onboard" stabilizer jacks are just that......stabilize! All trailers are susceptible to movement because you are still being held up by the suspension (springs). There will always be some degree of "bounce" movement when someone walks on the trailer.
The x-chocks will help forward & rearward movement but not completely eliminate it. The only way to eliminate vertually all movement is to support the trailer directly under the frame. The support jacks mentioned above are a good place to start (but that requires crawling under the trailer each time to set them up). So, IMO, unless you're parking the trailer on a lot for an extended period of time, it's not worth all that effort just for a weekend.
Most manufacturers don't recommend slide supports. The slides are designed to support themselves and any activity that may take place in them (ie; sitting at the dinette, couch etc).
Enjoy your 303RKS. We had a 2011 303 as our previous TT and thouroghly enjoyed 3 years of trouble free service & fun! 👍
"PT Crew Members Since 9/2010"
2011 RAM 2500 HD 6.7L CTD Crew
2014 Sanibel 3250