Those tires look way overinflated to me. Check the sidewall for recommended pressures which should be somewhere around 6-8psi. Overinflated tires would explain the hard ride. Cheng Shin tires always have worked well for me when it comes to a stock appearing replacemt tire and they still have the soft sidewalls for that soft cushy ride you are missing. If you really are looking for a soft cushy ride, you may want to try something with suspension. The 200e big red is a nice ride compared to a hardtail. You could always try to find yourself a suspension framed kit on a hardtail. A major step up in fun and comfort. And if you really aren't trying to ride the bike really hard, it can give you many years of a nice soft really cushy ride. You could even go as far as purchasing a rear shock custom tailored to your size and weight. I'm around 250 myself and really enjoy the ride over a hardtail. And then you have the added benefit of having something not everyone else has. There was a 200s frame with a weld on suspension kit on it on ebay. It would be a good start to a nice unique trike. Also you may want to look into adding a suspension front end to your trike which would go a ways to help cushion your ride. Do a search on here, but I would believe a suspension front end off a 185s or 200s would be a direct bolt on and also give you the benefit of a front brake. And they are usually not very expensive used.
Nicholson 500x (Project)
Nicholson 185s
Nicholson 110 (That takes an atc70 tank)
Ascott 500 head/350x (Project)
Homebuilt Racer Chromoly Suspension 110 (Ragin Runt)
PK Racing Suspension 70
A+ Inc Suspension 70
AWS Aluminum 90 frame
Hi Performance ATC Suspension frame rd350
Hi Performance ATC Suspension frame 90