Hoboscratch-
I farm yeast and have a similar issue. There is a field for what you are asking: "Times Cultured". The problem here is that its a field for the yeast item, not the inventory item. You can adjust this in the recipe, but I don't see much point in that.
I've settled on the following workaround:
When I culture, or wash yeast...I make a copy of the original yeast in "yeasts", and change the lab to myself "hampton labs". Then I increment the "times cultured" field, set the package date, and update the inventory qty. If I'm reculturing from my own stock I do the same thing. So, I have one inventory item for each generation I have in the freezer.
When it comes time to prepare to make a recipe, I a) Copy the recipe to the brewlog, b) Edit the recipe, and change the yeast to one of my generations of yeast from inventory, c) make any other changes before I brew, d) remove recipe from inventory, right before I brew.
It works, and I'm not sure if there really is a better way. The key point is to always move the yeast through inventory.