I guess it's difficult for me because I'm trying to accomplish 2 different things at the same time. I'm thinking maybe I'll just feed the packages alot and let them do their thing without stealing from the big hives.
IF you have comb to give that is an option.
Don't bail due the perceived difficulty.
3 or 4 days prior to the packages arrivial, do an inspection of the 6 prod hive, IMO taking 1 frame of stores and give 1 frame of comb or foundation would help with egg laying space for the prod hives, a full or mostly full frame in spring is not used for brood all year, and better removed.
A frame of fresh worked stores, is a good thing for the package to have, agree on the feed and pollen patty the 6 hives 3 weeks prior to package arrival, if the hives are packed a frame of brood could be used noting the need for treatment this may cause. You should wash and do counts this spring any way, as well, you have time to treat before the packages arrive.
stores frames are fine sitting in the garage for a few days. Brood frames need be pulled minutes before hiving the package. But the inspection will "show you" where they are can even mark them with a marker or something to easily find when needed.
You have the "means" to help the packages, push your self if uncomfortable, with the activity for the good of your new packages. A can of sugar syrup, when you have the 6 prod hives some maybe honey / pollen bound is opting for the base hit when you are capable of a triple.
End of the day it is your decision, I have boosted packages to getting 3 or 4 supers of honey the first year, while helping my other fuller hives to open the nest a bit. Hate to see your new packages struggle on syrup and the best 2 prod hives swarm due to a congested brood nest. the 6 prod and 5 packages is a prefect time to do some leveling and optimization if needed or wanted.
Also do check the packages in 3 week, and 5 weeks, post hiving, with 5 there is a good chance for a supercedure or 2, one could use the QCells to do a split on a too large prod hive or requeen one that needs it, if you like the genetics of the packages you have ordered.
good luck
GG