AMDs supply issues will be difficult to smooth out. They are using TSMC for their CPUs but they also have to compete with nVidia and Apple along with their own GPUs for products and of course any other companies that want to use TSMC for their products.
One route could be to go with multiple FABs, like Apple did with some iPhone CPUs a few years back, but that means there will be a much more pronounced difference between them and people will prefer one over the other.
Otherwise they will have to either hope TSMCs yields go up or they open another FAB to produce more chips. Either way it will take time and being unable to fill orders will hurt a bit.
They are able to fulfill orders, you only need to order six months ahead of time.
The "preferring chiplets from one fab over the other" thing has one simple solution: move entire product lines over (ex.: GPUs and APUs) instead of partial production to free up wafers on TSMC for chiplets. Another option might be to make every multi-chiplet CPU a mix of both for twice the silicon lottery fun.