I would say just plan for the supply depot to be depleated and work from there. Make sure your crew is carrying supply from a camp. Setup siege in ideal spots to preferably keep ram opperators off the gate at a minimum without being destroyed. of note, carts dont need LOS to hit a location, if you can angle your camera to see the ground you can hit that spot even from a safe spot away form AOE. Bonus note balista's can hit through doors if you can target something. Most rams get droped so they stick through the door a bit for a free target although you could also have someone on the wall calling the targets.
Either way leave enough of your buddies to main the critical siege locations and take whoevers left on a blockade running mission. A group of 10 with the ability to chain siwftness can get around quick. Go clean out a nearby supply camp, take it over if you must and then dash past the army knocking on your door. Arrow carts on the walls can do a good job of opening a path with suppressive fire tactics. Dont need to kill the attackers just distract em long enough for the runners to dash past. Use the supplies you gained in your run to make repairs or put up more siege.
Once the stockpiles are gone the pugs have basicly no way to hurt your crew. If your plan involves working around an empty stockpile your fine.
Personaly my plan is to do less on the heavy defending and more on wipeing out the enemy supply lines. Fast mobile strike force to slap yacks and knock over camps. after hiting a camp and apropreating the supplies either target something lightly defended or just drop off siege for a zerg and get right back out on the supply lines.