My experience with my P500 is one of not the "norm" I'm gathering from years on this site. I come from many years of riding 3-wheelers and sport quads. Therefore, I do not know what a "smooth" or "cushy" ride is. This is the first machine that I've owned with 4-wheel independent suspension, even though I'm told it is bad. OK, yes the P5's suspension has it's limitations because you can only put so much suspension in the space available. As for the tippy-ness and unstable: I only felt my machine had an issue when I was crusing in 5th gear at about 32 MPH and tried not to lift on some tight corners.
Biggest thing I can say is get some bigger tires that are radials- I have 26" Kenda Bear Klaw HTR's on my stock wheels and when I put those on the ride and handling improved 2 to 3- fold over the stock tires! I ran this set-up for close to 2 years on the 50" ORV trails here in Michigan and never felt like it was unstable.
Next, get rid of the rear sway bar. The bar is way too stiff for the machine and I found that every small bump/rut/rock/hole you hit with the rear, the sway bar transferred that hit right to the frame and right to your rear-end in the seat. I finally removed mine after 2 days of riding in Moab and figured out the swaybar was transferring the hard hits.
Between the radial tires and sway bar removal, I think my machine is way more stable and rides better than stock!
Now a few on here may remember that I did put 1.5" spacers on all 4 corners before my Moab trip (2021) but I've been too lazy to take them back out. I believe that I could remove them and be just fine. But these are not a high-speed handling machines, so my putting around on trails up north around 10 ~ 25 MPH it does just fine.