Add an event to allow overridding the generated variation title

I've been trying to figure out the best way to hook in and replace the title of my variations in code when they're saved. What I'd like to do is have it generate an automatic title, but change something about that title from another module in code automatically.

The problem is that we have some "N/A" attribute values, and the auto titles are ugly because they have sometimes repeated "N/A, N/A" values in their titles, and our client doesn't want those there (and I can understand why). Since their products are so varied that we can't really get around some attributes not applying to some products, and since attribute fields require a value, the N/A value was the way around that. it seems the only real way around the title issue is to override the variation titles and remove those N/A values.

I've tried ProductEvents::PRODUCT_VARIATION_INSERT and ProductEvents::PRODUCT_VARIATION_UPDATE but trying to set the title there simply has no effect, it gets overridden after that again if I have automatic titles enabled.

Is there a later hook I should use, or another recommended way that I could achieve the desired effect of modifying the auto-generated variation title (automatically, every time a variation is saved)?