How to mix large amounts of sponge for bread?
Our local large bakery has mixers that have a tiltable bowl: mix, lift the bowl (with a kind of crane), dump the content out - wherever it's supposed to go. But we are talking about five to ten times the amount you asked about.

For 10kg in total, you don't need a mixer. Roll up your sleeves, wash your hand and give the poolish a good mix with your hands in a large tub. I have kneaded similar amounts of bread dough (60-70% hydration) by hand and know others who have done the same. Your 100% hydration poolish will be even easier to handle. Then scrape off what sticks to your hands and let rest as usual.

Note that a poolish doesn't need dilligent kneading, gluten development happens during the long fermenting phase, not during kneading. So if the poolish is somewhat "shaggy", it's ok.