Forget AGM on a limited budget. Get a couple GC2 from Costco/Sam's. Try to find the gold lable version at 225 or 232 Ah vs the lower cost 208 Ah.
Consider ~150w of solar instead of the costly relay. Existing isolator will still get some bulk charge in and the solar still works all day on the road, stopped at various day destinations, and at camp if you have some sun.
Could just get a battery switch to manually bypass the isolator when driving.
IOTA + IQ controller will work great over the OEM fixed voltage. LEDs will seem to add 50%+ to the battery capacity.
Battery $200, Solar $250, IQ controller $25, LEDs $25, and you are in budget.
