Definitely sounds like tires and cold weather are adversely impacting your mileage. If you're not seeing recalibrations, then it's highly unlikely your IMA battery is adversely impacting your mileage.

There are other factors like spark plugs, O2 sensors, etc. that can adversely impact mileage by 1-2 mpg, but truly problematic issues will throw a CEL or IMA light.

I recommend EP422 Plus now (non Plus is no longer available), and not putting them on all 4 wheels will likely result in little benefit. While they are my favorite, any budget friendly low rolling resistance (LRR) class are likely vastly better than what you have now. also consider over over recommended pressure, but under sidewall pressure. I routinely run 40psi in all my hybrids even though they may recommend 32-36 depending on the car.

Make sure you start with a fully charged 12V before you start (place on charger overnight at a 2A setting if that's an option), and periodically check your 12V during the grid charge (with the 12V charger on 10A setting). If it drops below 11.0V, pause the grid charge and turn the car off for 2 hours to let the 12V recover at a 10A charge. Starting and stopping grid charges do not adversely affect the process provided you do not drive the car in-between. Again, make sure everything is off while the key is in the ON position. Blower off, lights off, etc. if there's something stubborn that you can't turn off, you can pull fuses. You might be surprised how much juice a car can pull just sitting there. Heck, even 100W of power requires nearly 10A of current, and I think the blower requires 8A when on full blast, though it will likely never get there. With a little luck, you'll only have a 2A net draw, and you'll be able to run that way for 20 hours.

A simple charge/discharge cycle can't hurt. Do not discharge below 106V. If you're not in a hurry, just stick with 2 low wattage bulbs (60W) in series and let it play out over up to 24 hours. If you record times with voltages, we can estimate the capacity of your pack.

Hang in there. My son attends ASU, and they are online-only for the remainder of the semester. The public high schools are working to deploy an online-only curriculum to let them finish out the school year at home. My daughter is losing her freakin' mind as this happened immediately following their spring break, so she's been out of school for 3 weeks now.