I know you aren't looking to spend more money, but this unit looks a bit under-powered.
If you want fire-and-forget, go with another 100w panel (Renogy makes a good affordable one, Amazon for ~$100) and add that to your set up. (You'll need a 2-1 cable, maybe $10, assuming that kit uses standard solar panel cables) That alone MAY be enough to get you over the hump.
Also, 2 x 6v batteries in series (such as golf cart batteries) is almost always better than a single 12v. A little spendy but, generally can double the amp hours of the set up.
By way of reference, I run 4x100w Renogy panels with solar controller and 2x6v Duracells in my Class C motorhome.
The entire set up was about $700 and will power my entire motorhome non-stop with zero need to run the 4k genset pretty much indefinitely, unless I want to run A/C while not on shore power.
Good luck!
These are 100 watt Renogy panels. I don't mind adding another battery if that would fix it. It's just a pain in the ass when I don't understand electrics and the panel is rated at 100watts, the battery is rated for CCA or Amp hours, the Charger need 650 mA on full power or 350 on half power... None of the ratings match up for me.
I have 2 chargers, 2 batteries, and 2 panels... Cows in 1 field, SO i can double things and experiment.. Might need a larger regulator if I double the panels, I have a 10 watt, but they are cheap.
