Hi,
Well, combining multiple filter plugins is probably not going to work this way, it is usually not a good idea. Each plugin does it’s own thing, overrides the results etc.., and in the end usually only results from one of them are displayed (as they simply override each other).
I am not sure if it’s worth trying to make them work together, as fetching results from one and then plugging it to the other to filter is a very difficult task – in most cases not even possible.
The biggest issue here, is that ajax search pro is instructed to redirect to a page, whereas the other plugin tries to reach the shop page and filter that – which I guess it was made for. And even if that is resolved, I highly doubt combining them will do any good.