A simple solution is to ship a Refueling Station to the innermost moon of the gas giant, and build a cheap tanker (or a small fleet of fighters or FACs with nothing but fuel tanks and a weak engine on them, even,) set up with orders to just constantly load fuel from the harvesters and deposit them at the colony. If you use fighters or FACs you'll need a little more ground infrastructure, a maintenance facility or three and enough population (and infrastructure/LG infrastructure) to support them.
This isn't hard - even on a world with a 9. 0 LG colony cost world I found it trivial to get enough LG infrastructure on the rock to support a few maint facilities. Minerals are lightweight; just ship in a little duranium, gallecite and uridium (one trip from one of your freighters; the only thing you'll have to move with your own freighters, as civilians can do all the heavy lifting of the refueling station and maint facilities), and they'll crank out the maint supplies the little ships need. And given that you can get maint lives of years on FACs and fighters that aren't lugging weapons and use a small engine, you shouldn't have a problem. (Using conditional orders to ensure they'll top off MSP is a good idea, and make sure they have enough MSP on board to repair their own engine. )
Or you could skip all that and just tool a commercial yard to build a cheap tanker with very weak but fuel efficient engines. Or just dedicate (or build) one of your normal tankers if you've got a yard tooled for it already. Or build an extra commercial tug for the sole purpose of leaving it at the gas giant, so it can drag over the odd harvester to empty it onto the rock if your tankers are late in getting there.
Or build a separate station that's just a refueling system and some big fuel tanks and leave it on the gas giant, but not in the harvester's fleet - if, on occasion, you need to preferentially empty a harvester, detach them from the fleet, order them to refuel the big floating fuel tank, and then drag them back into the harvester fleet when you're done. It's micromanagement but you shouldn't have to do it more than every couple of in-game years, typically.
Note that the gas giant moon option is a lot more attractive in C# than it was in VB6, because it's a LOT easier to get surface-to-orbit weaponry onto a rock now (no long grueling construction of PDCs with construction units); which means that a close-orbiting moon (or one where you left a tug) can provide on-site protection for your precious harvesters should some NPRs or spoilers show up without an invitation.
EDIT: If you're desperate, you can separate out the harvesters that are mostly full into a separate fleet, and order them to refuel the mostly empty harvesters. Advance time hour by hour (or three hours by three hours) and watch the fuel carefully, then cancel the order and have one fleet join or absorb the other one when you see the fuel is somewhat equalized.
