Search Vaiable Products by SKU?

My site has a ton of variable products, but the kicker is that customers search only by SKU numbers (it’s the only option based on the business). Currently I’m using Relevanssi to index the SKUs so that it is possible to look up single products.

Due to the fact that this doesn’t work with variable products I have all my products as single products, but this is super inefficient as I have about 850 products right now. It would be extremely helpful to me and customers if I could change the products to variable for size color etc etc. But it just won’t work if I can’t look up by SKU.

Any ideas would be greatly appreciated!