How can I manage stock levels for product variants in one pool?

Is there a way to turn off or bypass each variant option of a product having it’s own stock level, and instead draw from the parent product stock instead? For example, one of our products is Frames which we want to offer in Packs of 10 or Packs of 50, and also have the option to choose to buy them Flat or Assembled. Essentially 4 options:

10 Pack - Flat

10 Pack - Assembled

50 Pack - Flat

50 Pack - Assembled

However these are all options of one product; the Frames. We want to be able to set the stock of ‘Frames’ and the options to pull from that stock, not their own. For example, say there are 100 Frames in stock. When someone buys one of the options, it deducts from that 100. We make the Frames in-house, so each variant option is coming from the same stockpile.

There doesn’t seem to be an option to set a stock level for ‘Frames’, only each of its 4 options. Each option does have it’s own price as well. Is the best solution to this to just use the same stock level for each option - eg setting each option to 100? Because if you do this, Shopify then says there are 400 in stock which isn’t true.

We don’t want to go down the route of making each option it’s own separate product either because that creates the same problem with stock levels. Is there a solution to this?