Get forks and bucket with the rental.
If you're creative, you can extend the bucket with small diameter logs sticking forward, like forks, that are pointed against the top, inner part of the bucket with other logs. This will be for manual loading.
A rope-choker to drag limb piles will help.
You may be able to set the limb butts on the chipper tray, if you have his techniques. You may want to jack up the chipper tongue to lower the tray height.
Thin (3/8-1/2"), shop-grade (discount, defect) or scrounged plywood works effectively and economical for a turning platform if you have lawn/ hardscaping, etc. to protect. 4x4' can work.