I have a very small front yard (300 Sq. Ft.) with St. Augustine. There are thin spots and it looks like it's possibly due to heavy thatch. I've read mixed things about dethatching St. Augustine, but did it anyway in a few spots. So question is do I dethatch more, let it grow in (fertilized a couple weeks ago) overseed or other? And a little additional, the whole yard gets the same amount of sun (full).
If you already dethatched, then the route you take will depend on how patient you are. If the spots are bare, you can nurture the existing St Aug and allow it to fill in the bare spots. Be sure to use a good pre emergent to keep weeds at bay while the St Aug spreads to fill in the bare ground.
If you are an instant gratification type of person and not willing to wait the time it takes St Aug to spread; which could be the entire summer - depending on how large of an area you have to fill in, then you can put a piece of sod to fill in the area. We can buy St Aug by the piece where I live, so that would be the route I'd take.
Since you can't buy St Aug seed, I'd discourage putting any other type of seed down, simply because I like having a single cultivar in my yard when possible. But that is an option.