Usually 3 rubber bands will do. You can add as many more as you like , but each one will potentially crush a line into the brood comb. Size 16 is a perfect fit for the height of a full depth frame and size 32 lengthwise.
I’d suggest, before jumping straight into cutting up the old brood, remove your Flow super and your jammed up box and put your fresh brood box in place instead (with the Flow super back on if you’d like). Shake your jammed up box out the front of the new hive set-up to dislodge as many bees as possible who should start walking back inside. If you then place the old brood box with frames on it’s end, and facing into the sun the rest of the bees may follow their mates and walk back into the original site over the next half hour or so. If you’re lucky the original shake may include the queen and you may see her walk back in to the original hive site.
If I knew the queen was on the new frames, I would then re-arrange my boxes with jammed up box at the bottom- then queen excluder -then box of new frames with the queen, topped with the flow super (over another excluder if you have it). After 21 days any brood in the jammed up box will have hatched, and you can then hack away without fear of damaging brood and any extra comb you cut off can be crushed to extract the honey. Meanwhile the queen has hopefully spent 3 weeks laying brood on fresh frames.
If the bees all move off the jammed up box, you have the choice of doing the above or cutting and correcting the wayward frames straight away. If the bees don't all move off the jammed up box, at least you've reduced the numbers on the frames and means fewer to crush as you pull the old frames out to clean up.