Wood chip size is largely a function of the blade(s) edge to anvil difference and blade edge to flywheel face distance. I have a 3"-maximum, stand-alone
chipper-shredder that produces 1/4 - 1/2" chips; the anvil is set about the thickness of a business card from the blade which extends about 1/4" from the face of the shredding drum. Small, around 10 hp chippers have only enough power to shave the ends of 3" logs. My 6" Salsco calls for a blade to anvil distance of 1/16 - 1/4" . It is set for 3/16" and produces much larger chips, some as large as a deck of cards. Both PTO chippers I have used, a 4" Wallenstein and the 6" Salsco, produce chips larger than the setting. I attribute that to the greater distance between the anvil and the face of the flywheel or between the blade edge and the flywheel and slack space around the infeed throat and the blades. Pliant twigs are usually spit out like "birds' nests".
My tractor has 32 hp at the PTO and no problem with the Salsco and its heavy flywheel.
I suggest borrowing or renting a 4"-6" PTO
chipper and seeing if feeding chips through a second (or third) time reduces them to the size you want for bedding. Feeding multiple times will likely be more efficient than frequent blade adjustments.
Chipper-shredders that macerate leaves and small branches, typically with a hammer-mill, are more expensive than chippers (only) at a given throat size but may be another solution. If possible, try before you buy.