Most likely the PSR-353's sound engine would come very close to responding to the full range (0 - 127) of MIDI velocity levels - probably closer than most of us would guess. That part of the technology has come a long way in the past few years, but as we have already discussed, its problem is the keybed. At the low (soft) end, the PSR-353's keybed would cease generating signals to the sound engine while a real piano or a weighted keybed would still produce a very soft audible sound. At the other (hard) end, one of two things happen. A real piano will generate a sort of "twang" on the middle to lower notes, when struck very hard, or the wooden hammer mechanism will produce a very audible "clunk" when the higher notes are struck with the same force. The PSR-353's keybed would either never reach this threshold to produce these sounds (most likely) or would reach this threshold way too soon (least likely). Where a good weighted hammer action keybed might be able to reliably produce velocity values of 10 or 20 to 110 or 120, the PSR-353 would probably only be able to produce 20 or 30 to 90 or 100. So you can see, whether you are using the PSR-353's internal sound engine or an external sound module or software sound engine, your playing dynamics are still limited by the dynamic response capabilities of the PSR-353's keybed. Whatever the case, I think if you follow Michael's (SeaGtGruff's) suggestions, you will certainly notice an improvement, with just your current setup, over what you have been getting.
Now, so that we don't leave you feeling like we have pulled the rug out from under you, I will tell you an anecdote. Some years ago, a very animated Dutch fellow by the name of Bert Smorenburg, who normally demos high end Yamaha gear, and has a reputation on several forums as having the ability to sell rectangular tires, introduced an entry level Yamaha synth with several wave samples from the original Motif model and a set of DJ type real time sound controls. It was known as the MM6, and provided the proto-type for the current PSR-E4X3 models. It also introduced the body-shell style for the current PSR-E3XX and E4XX model lines. I have a very strong feeling that it also used the same, or very similar, keybed as these current models. Typical of Bert's demos, he started with the marquee grand piano voice. You would not believe the dynamics he got from that keyboard. The point is, if you can learn to live with your keyboard's limitations, you can learn to exploit them to their utmost.
Best of luck !
Regards,
Ted