What you're looking for is small business warehouse management applications which certainly exist although to your point they're rarely simple unless they're, well, simple. This is because of the extreme variation in how products are handled... as you scale up the implementations become larger but more standard [there's specific events / training for this stuff].
If you're not doing anything to manage inbound & outbound inventory that does put you in a good place as you can find a total solution rather than pieces. Essentially this will start with recording [either by carton / scanner / manual entry] inbound shipments, matching those against orders through an API from your order management system [OMS] and ideally hook into shipping to "know" what's outbound. If you have a pick, pack & ship team you'd want it to go one step further and cross associate their scans as they fill orders. This all loops back to your various partners through the OMS or directly to keep inventory accurate either in real time or frequent batches so you're not risking overselling.
Cross platform sales should not be an issue so long as orders funnel back into a central OMS. If not then you have to hook into each place which is a pain for integration and essentially would turn your warehouse management tool into your OMS... Essentially you want a place all orders are held, all customers are merged, and all products live that feeds in and out of everything else.
Of course my answer implies some level of scale. If you're really small you're not likely to find a dedicated program that will fit your needs AND budget but a good central OMS can handle the basic counting and help prevent out of stock.
Since you're in CO you may want to check out shop.org's conference this September. It's a great place to hear about the latest in ecommerce best practices as well as meet a lot of vendors in the space.