Recently our farm has been overrun with red squirrels. These are the little guys that like to eat electrical wiring out of tractors(they chewed the main harness out of our newer JD to the tune of $1000 and a neighbor had over $10k of damage to his machines).

We had been using rat bait but not sure on success or if they are just stuffing it places. Would like to go away from that due to our dogs potentially ingesting or squirrel dying and dog finding.

So more looking for trap and bait recommendations. We have tried live traps with peanut butter/nuts/veggies etc but no dice.

Feed ‘em some .22

I'm surprised you don't have a healthy population of predatory birds.

Tube traps. Most of the online trap vendors will offer them. Bait with shelled corn or birdseed. Be sure to anchor your trap so some larger animal doesn't drag it off to eat the dead squirrel.

https://www.youtube.com/watch?v=YTzu12XN054

And another
https://www.youtube.com/watch?v=dGQzMEyBRNs

Have resorted to 12 gauge. They are fast and much more twitchy than standard issue squirrels.

Usually our dogs get a few on the run too. Not these

Snap traps. Hot-glue pistachios or almonds to the triggers.

Rat zappers/electronic traps. Some even have wifi to tell you when there's a tree rat in them.

Always wondered about the skull crushers:

Old school victor rat sized snap traps do great on red squirrels. Put peanut butter on the pan and a half a shelled peanut or birdseed on the peanut butter.

If you need to put them on ledges or beams drill a pilot hole and screw them to it.

Colony traps work but are expensive and kind of a pita.

Lately I've had good success with Koro Rodent traps.  I modified the box enclosure others have used on squirrels for chipmunks.  I have never had one trigger without killing the rodent.  I plan on moving on to  squirrels shortly.