The IEEE 802.11 standard does not specify how a client should determine which AP it should connect to; it's left up to the equipment vendors as an implementation detail.
Clients usually just connect to whichever AP has the strongest signal coverage where the client is. It might be interesting to use a tool that does 802.11 scans and reports the signal strength (RSSI) for each AP it sees (and breaks them out separately even if they're all publishing the same SSID), and see if your HP AP's signal is stronger from the client's perspective.
Enterprise-class equipment vendors understand your predicament. If you want to maximize bandwidth for a lot of clients in a small area, you want to put APs on 1, 6, and 11 in that area, and have roughly equal load on each of the APs. But there's no way in the standard to guarantee that clients will do what you want unless you set separate SSIDs. Some vendors of enterprise-class APs have shipped features that try to work around this from the AP side, and some vendors have tried to get client card vendors to be sure to work with their system (example: Cisco's CCX program), but I'm not sure how well any of these attempted solutions really work. There's even been some work on addenda to the 802.11 spec to help clients make better roaming decisions, but I'm not sure how well those things have been adopted.