IME the quickest way to refuel a carrier is to have multiple Cmdr passengers travelling with you, at least some of whom are good at mining.
Out in the black I've never come across a double hotspot or anything like that but actually finding a trit hotspot in an icy ring isn't that hard.
I use a 512t shieldless Cutter with reactive armour hull, 15 (?) collectors (one module is a class 3 universal limpet controller) & a 2 prospector controller. I have four C2 regular mining lasers, a c2 SSD gun, an abrasion blaster & a core mining gun (no regular weapons needed out in the back), It also has a DSS & PWS of course and the power distributor is weapons focused.
Hull damage is a thing that happens, especially while doing sub-surface stuff but I'm not mining for profit so I just repair the ship each time I dock.
I used to drop in close to the centre of the hotspot for better laser mining & opportunistic SSD & surface mining but lately I've been dropping in further out (at least 1MM) and doing a lot more sub-surface work. It is at least 30-50% faster but with no shields I tend to take more hull damage while orbiting a rock, and I use a lot of tungsten rearming my SSD gun 5-6 times per run to fill such a big cargo hold so I am trading off mining speed for surface prospecting speed (the rest of the mats fill up while mining icy rings).
I have tried different ships & loadout variations, this is the least compromised way I've found when doing it alone. If there's more than one of you in a team doing it you can double up on prospector limpets and laser mining (you both shoot the same rock using only one prospector & both get the full amount, SSD & surface stuff doesn't duplicate).
I always completely fill the carrier buying trit in the bubble before I leave for a trip, mining is nice variety while out on a long trip but it's something I only do because I need to, I don't particularly enjoy it. I would be very happy if trit mining were as productive (in terms of tonnage per hour) as Plat mining in a metallic plat hotspot.