Sometimes our minds get fixated on a plan and when design problems arise we tend to expand the plan to compensate. I have found from some of my wilder designs that at some point it expanded so far that it was really not worth it considering what the original plan was designed to accomplish.
You want to keep batteries warm but your plan is so expensive that it just makes sense to go with simpler options that actually work better. An above ground insulated structure that is easily accessible and well insulated can hold heat from a heating system with minimal power.
Remember that the critical point is making sure the batteries are warm enough before they start charging. They have several batteries out there that have built in heaters that will draw power from the PV array and heat their enclosure. It is only when the batteries reach the proper temperature that they will start charging and the charging will produce enough heat to keep the cabinet warm.
In a nut shell I am saying use half of that money your going to spend on the underground system towards batteries with built in heaters or an enclosure that is heated by the panels or it's own set of panels.
If it's so cold and snowy that you have no PV then your underground system is not going to make a difference anyway. If your plan is to use a generator to power the house and charge the batteries then that same power can heat the battery cabinet and also charge the batteries. Keeping a tightly packed well insulated cabinet with batteries inside of it warm is not going to require a whole bunch of extra power and it's far cheaper and much easier to access.