Unable to connect iPhone 4 properly to Time Capsule

I am unable to properly connect my iPhone 4 (running iOS 4.2.1) to my home network running a Time Capsule. My iPhone 4 shows the network. If I click on the network to connect, often after entering the password I am told the iPhone is unable to join the network. Sometimes, I can connect, and I get realistic values for the phone's IP address, DNS, and other items, but after a short time, I can no longer do anything that requires WiFi. The WiFi symbol still shows, and I still appear to be connected, but surfing a web page, going to Facebook, etc., just hangs.

I completely re-set the Time Capsule back to factory defaults. I've also completely wiped the iPhone clean and restored it from scratch (as well as resetting all network data, and forgetting my home network and re-adding it). None of these procedures has changed the problem behavior.

I've gone to an Apple Store and spoken with a Genius. While there seemed to be no problem with my phone, I was given a new one (great service). The problem remains.

The Time Capsule is a simultaneous Dual Band II. It runs 802.11 n only on 5 GHz, and 802.11 b/g only on 2.4 GHz. The two networks have different names [MyNet and MyNet (5 GHz)]. It runs WPA2 security. It is set for wide channels (turning this off did not help), and channels are selected automatically.

I have several Macs, an iPad (running iOS 4.2.1), an AirPort Express N, and an Apple TV (first generation), an Apple TV (second generation) that have no trouble getting on MyNet (5GHz). I also have a Blackberry Bold 9000 that has no trouble getting on MyNet (using 802.11 g).

The Time Capsule is running in bridge mode because my home internet is FiOS, and comes into the house as a MoCA cable connection without ethernet, so the FiOS router supplies the ethernet connection to the Time Capsule. The FiOS router supports WiFi, but only 802.11 b/g, so I usually turn it off and let the TIme Capsule run the WiFi. The FiOS router performs all DNS activities.

This whole setup worked flawlessly until recently. I have the Time Capsule visible through Back to My Mac everywhere I go, and all my other devices connect just fine -- as the iPhone used to do. (Could it be the recent firmware upgrade for the Time Capsule?) Everything still works flawlessly, except for the iPhone 4.

When I enable the FiOS router's independent WiFi (b/g), running WAP2 with the same password as my Time Capsule network, and have just the iPhone connect to that network, all is perfect.

I'd prefer not to have to run the FiOS WiFi network JUST for the iPhone, since I'm in a fairly dense development with LOTS of WiFi near me and want to avoid even more congestion.

Does anyone have any suggestions? The Apple Geniuses say the next step is to replace my Time Capsule, which I will do after backing up its backups, but it seems that there is a problem between iOS 4.2.1 and the new (7.5.2 Time Capsule) software. I'm guessing, since I can sometimes connect but then lose connection, that this is some kind of WAP2 problem, but all my other devices work just fine. I do not want to run a non-protected network, or a network protected with WEP or WAP, since they are older and less secure protocols.

Thanks in advance.