The best I think will be to use both weight and volume restrictions:
You set high volume, no weight for one group of products, and no volume, high weight for the other.
Then, you create three sets of shipping methods:
one for high volume, no weight with the shipping fees for the one group of products
one for no volume, high weight with the shipping fees of the other group
and a third group with both high weight high volume with shipping fees summed up for when the two types of products are in the cart