I have a similar problem with mattresses and mattress sets. A dozen different models, each with at least seven different sizes and either sold separately or as sets with a box spring--which offers even more choices.
The number of ILCs required is insane and there is no good workaround, especially since you can't print price tags for assembly items.
Assembly is the way to go. Kits will take the components out of the item inventory and need to be broken in order to sell the individual pieces. I assume that you do not stock a bag for every ball. I know that I don't stock a box spring for every mattress.
Until MS fixes the Assembly Price Tag Issue, you can limp along like this: Create a separate database with the same ILCs as your assemblies. Use the same pricing and descriptions. You can print price tags from this database.
Oh, and search this group to find a thread where you can vote for 'Print Price Tags for Assemblies'.
HTH, Tom