Cleaning a pendulum/traversing pitch with a modded grigri

If I lead a traversing pitch, lead rope solo, what, if any, is the best way to get back to and clean the gear/untie from the lower station before jugging and getting ready to lead the next pitch. I may or may not have enough rope to simply rap the extra line, especially after linking pitches. Not to mention i might be too far to the side to just rap. If i wasnt, i could just rap the lead line.. and I wouldn't have a question. I do not carry a tag or lowerout line when soloing. My 'hauling' is done as I untie my lower anchor and jug the lead line with a backpack full of food and water, which, always stays at the lower anchor. I'm trying to not re-aid my pitch or do 10 lower outs. Anybody know anything that is fast??

Thanks!

carry a second "mock haul line". fix it at the lower anchor, lead your climb, fix it at the upper anchor, rap it, transfer back over to your lead line, untie the "mock haul", jug and clean. (and hope it doesn't wrap up around something while you're cleaning.)
i dont know how you could quickly and easily clean a traversing pitch with only one line. i always solo with two lines.

Thank you.