You can remove the fiddles but lose function of keeping things from rolling off the table. The fiddles that run athwart ship are the real offenders with sleeping comfort. They don't need to be very high to do their function. You could rip them down on a table saw or plain them in place to a more comfortable height. If they are glued as well screwed, removing them all together may cause damage to the table material that could get expensive to put right depending on your aesthetic tolerance.
Putting thicker cushions on may make the dinette uncomfortable to sit at, btdt. Accomadation tolerances on a boat are usually very tight. Do your homework before going that route
You could also try harder foam for the cushions. Personally find the foam used in boat cushions too soft. Blasphemy, they painted it!!!! Most endearing about the boat was its industrial chic oxidized finish in WW. Your butt bottoms out and sitting on them for lengthy periods becomes uncomfortable. Harder foam could kill two birds and you wouldn't valve to have new covers made.