If she is flying with you, in all likelihood an agent with grant her free bags (though unless you are independently exceeding your limit you can always just check the bag under your free allocation). For SkyPriority you just have her board with you when they board D1 and the agent won't bat an eye. Pre-check as stated isn't in DL's hands -- but you could always forgo your own PreCheck and take her through the SkyPriority lane at JFK/LAX with you.

For upgrades -- award tickets are eligible for F/D1, at least they have been in the past. I had Mrs.Duke787 added to the SFO - SEA and SEA - RDU waitlists last year when I had a business trip to SFO and she was on an award ticket and both flights they added her to the DoD airport upgrade list and we both cleared. Main difference is in that case I wasn't in paid J so was also on the upgrade list where it sounds like OP will already be in D1 so don't know how that impacts this scenario.

JFK - LAX is on a the 763 anyway so being stuck in Main Cabin should be fine unless Mrs.Adelphos is tall. You could always swap with her onboard so you still get the J miles but perhaps you take the J seat in one direction (to your work event) and she gets it on the way home?