As to your question whether a BXA QCTP will work with a 9" lathe, the issue is whether a tool placed in the tool holder will be at or below the spindle center line when the tool holder is at its lowest position which is usually the top of the compound. If you go to one of the vendors for BXA tool posts, you will find dimensions for the tool holders and you can compare the height of the bottom shelf of the tool holder plus the tools you expect to use with your spindle to compound distance.
For example Shars shows a 1/2" height for the shelf and with a 1/2" tool bit, the minimum height above the compound that the tool can be set is 1". If the centerline to compound distance is less than 1", you will not be able to set the tool to the centerline. You could, of course, use 3/8" tool bits which would then put the minimum height at 7/8".