Actually you could *technically* direct stage AP to BP. Basically I'm saying it is possible. And grain geometry isn't an issue in my theory. All you need is a short delay grain. Let's use an F21-4W as an example. Remove the ejection charge cap, add a little more BP and tape it to any BP 24mm motor just as if you were direct staging two BP motors. As long as it doesn't turn into a bonus delay and as long as your rocket is light enough to coast a few seconds before staging, then you'd get a nice composite boost, a four second coast (or less if you can correctly cut the delay down), and a nice stage. I know this method works because I've done the same thing with A10 motors. I removed the EC cap, added more BP, and taped it to an upper stage A10. Boost, coast, nice pop of the BP and a great stage. It was a cool effect with the delay. So really, the booster motor propellant doesn't matter with this direct staging method as this utilizes the delay and ejection charge of any standard motor. So in closing, yes you can technically stage APCP directly to BP by basically adding more ejection charge to the booster and removing the ejection charge cap, and you can do it with BP motors too. Makes a great boost-coast-more boost effect.
While I'm at it, you can also *technically* turn this around and direct stage BP to AP. As long as the motors are the same diameter, and the BP motor is a booster motor, or has the ejection charge cap removed with more BP added, then you could just tape an AP motor with sheathed thermalite or pyrogen tipped quickmatch inserted into it, and extending out the back about an inch so it can come in contact with the burn through of the booster motor or the BP of the enhanced ejection -or in this case "staging"- charge. That could work...technically.
Mind you , this is all just theoretical except for my "A10 experiment". I'm just saying that technically, it can be done.
Whew.