Gently coax them to one side of the cage. Clean the empty side, then coax them over to the clean side and clean the rest which is dirty.
I have had most of my pigs over a year and they're really comfortable with me around and that is how I still do it. Normally play tug of war with Po and Jupi as they want the dustpan and scoop. Lots of popcorns which results in them normally jumping into my arm sending poops everywhere. Or the girls and Basil will make a point of exploring under the fleece before I peg it to the correx to prevent them from going underneath. Or Mia will casually plod out the cage when my backs turned and explore the room before taking her sweet time plodding back to a clean cage. She's so not bothered, unless you pet her then she'll headbutt you.
Enjoy this time where you can spend 5 mins on a full clean, before long it'll take 30 minutes to an hour because theyve done something to slow down the process. Normally something entertaining and will leave you in stitches.