Hi Ted, California 14ers are different monsters than the Colorado variety and I say that with experience! I might recommend not attempting the Palisade Traverse from the JMT. The climbing isn't especially hard but the route finding is critical and the rock is not always pristine. You'd likely want some light climbing gear as well which I can't imagine you'd want to backpack with. Another problem with the Palisade traverse is that you'll want to finish it in a day, otherwise you'll need to bivy and water isn't readily available. If you are going to do the traverse, I'd set up a "base camp" at upper barrett lake then ascend to thunderbolt pass to start the traverse. The talus SLOG after Sill might very well be the hardest part of the traverse!
If you decide not to do the traverse and still want to hit a Palisade 14er I'd set my eyes on the southwest chute route on Sill. No technical gear required and the views are amazing... but you do have to contend with a hideous talus slog, both ways. You might also consider North Palisades West Chute or Clyde Variation of the West Chute.
Middle Palisade isn't a reasonable option from the west side as a JMT peak-bag. The rock is very loose and the climbing is precarious. You'd want gear, a helmet, and probably a partner.
A little bit further south you have Split Mountain which you should absolutely run up. Not technical in any sense but it's a very nice peak to bag with a good view.
Further south are Tyndall and Williamson. These are both easily attainable from the JMT and both could be done in one day if your route finding is solid and you're quick on your feet. Start with Williamson (it's more technical/committing) and go up the west face. The chute on the way up the west face is a scree/talus slog but once you get to the head wall you're met with some fun sierra 3.11a to the summit plateau. Tyndall is a little bit less committing and takes considerably less time. Go up either the Northwest Ridge (less technical, but longer) or the North Rib (more technical, faster). The North Rib has some very interesting climbing. Highly recommended!
Russell should also be considered. Going from the wallace lakes (stop here if you like to fish... was passing by here on the Sierra Crest Route last year and the fish were HUGE) your options are the North Ridge or East Ridge. Both are wonderful Class 3 climbs. The east ridge is a little slabby at points and throws some impressive exposure your direction but is not very technical. From the summit you could either descend back to the wallace lakes or descend the South Face Right Side chute which tops out between the summit ridge boulder crux and the east summit. You might also consider ascending the South Face Right Side Chute from Guitar Lake. Full disclosure, I've never down climbed the south face chute, only ascended.
Whitney is pretty obvious! Also hit Muir since it's right off the trail. Start where the cairns are. It takes all of 15 minutes.
For spice you could even include Langley if you're willing to walk along the PCT a few extra miles. Downside is no warm burger to welcome your return to civilization. Langley could also easily be ascended in one day via the Cottonwood Lakes/Army Pass trail.
If you do the Thunderbolt to Sill Traverse, Split, Williamson, Langley, Russel, Whitney, and Langley... that's all but one Sierra 14er! Throw in White Mountain Peak as a post JMT "warm-down" and you'll only have two California 14ers to go!
Hopefully some of that was helpful!