Here's my humble .02:
I have owned several boats over the last few decades, all had 12V ShurFlo pumps, like the pods. All had flexible hose for water lines, not semi-rigid tubing like the pods. Some had an accumulator tank, some didn't. One boat went through 2 pumps during the time I owned it, so I got to compare the original ShurFlo pump with a similar model 15 years newer made by the same mfr.
They were all noisy. It's the nature of the beast, IMHO.
I'd give the mousepad a try. I did this on mine and it did cut down noise a small amount, but the mounting screws still go directly into the pod floor and transmit vibration to the pod. The pipe insulation mentioned earlier will help a bit, serving to isolate the tubing from the pod's structure in specific areas where they contact each other. The tank will make the pump a little less irritating by stretching out the time between cycles a little.
A new pump definitely won't help, and I'd bet that neither will the hose isolation kit you mentioned. The most effective solution, I think, would be some sort of soft flexible "motor mounts". The mounts would screw into the pod floor, and the pump into the mounts, with flexible material bonded between. Your idea of plywood sheets with rubber between should help as long as you use different screws to mount the base to the pod than you use to mount the pump, leaving the rubber middle layer completely free to move.
Let us know what you decide and how it works out for you. If you make a successful mount, be sure to take pics as I may want to steal your design, ha ha.