The temps swings don't matter for while using the batts, but you will want to set the proper voltage for when recharging the batteries using the converter and generator.
That would most likely be in the morning daytime, so if 14.4 is about right for what that temp usually is in the forenoon (use less than 14.8 if it is over 77F at the time), you could get a 14.4v PD converter with CW. Or to do it right no matter what, get the PowerMax LK (which is cheaper too).
Solar is just to extend the time between generator/shore power via converter recharges, so upgrading the solar controller is not vital really.