I've had some further progress, but ultimately unsuccessful in using my SimpleMobile SIM in my Verizon iPhone 4s.
Here's some background: This was a brand new shrinkwrapped iPhone 4s and came with iOS 5.1.1 already installed. It was never used prior to starting this adventure. I had to connect it to one of the phone numbers under my Verizon plan because otherwise Verizon wouldn't unlock it for international use. Once Verizon unlocked the 4s, I immediately took the 4s off my plan and all I have done on the 4s since then is try to "fully" unlock it for use with a SimpleMobile SIM. I really only need it for international use, so if I can't get it to work on SimpleMobile, it's not a big deal. Just a side project.
As stated, after Verizon told me they had unlocked the 4s, I took it off my Verizon account. (I'm restating this in case you need to have the phone active under a Verizon plan for all this to work. I don't see why, though.) I removed the Verizon factory SIM. I inserted an international SIM and connected the iPhone 4s to iTunes 10.5.3. I got a message stating the the phone was unlocked. I inserted a SimpleMobile SIM and the phone gave an "Activation required" message. I connected to iTunes again, but this time I got a message that "The SIM card that you currently have installed in this iPhone is from a carrier that is not supported under the activation policy that is currently assigned by the activation server." I reinserted Verizon's factory SIM.
(Whenever the iPhone 4s reads "Activation required", as soon as I open the SIM tray, the message will go away and I can use the phone again. Also, whenever I insert the international SIM, I never get an "Activation required" message and the phone will always read "No service" in the upper left corner.)
I proceeded to jailbreak and update Cydia. I also added RecoveryGuard through Cydia so I don't accidentally update from 5.1.1 to iOS 7.
Then I used iFunBox to make changes to the filesystem as described by WhiteSpir1t above. In my case, for a brand new Verizon iPhone 4s with iOS 5.1.1 pre-installed, I found a few details different. But first, if you are backing up carrier bundles and plist files and such, make sure you set iFunBox to disable binary plist (bplist) conversion from binary to ascii by navigating to the Help->Troubleshoot menu. Second, I define the CDMA antenna as disabled if a Verizon signal doesn't show on the upper left corner of the screen. If it's possible for the CDMA antenna to be disabled, but for the upper left corner to still shows bars and read "Verizon", then I don't know what I'm doing.
I found that deleting the plist files from /var/wireless/Library had no effect on the CDMA antenna. The only way I could disable the CDMA antenna would be to delete the Zeppelin_US.bundle folder under /System/Library/Carrier Bundles/iPhone. In fact, I could leave the plist files under /var/wireless/Library there, and as long as I had delete the Zeppelin_US.bundle folder, the CDMA antenna would remain disabled. Furthermore, the plist files under /var/wireless/Library would only regenerate if I had the Verizon factory SIM inserted. So, if I had deleted the plist files under /var/wireless/Library, left alone the Zeppelin_US.bundle folder, and the SIM tray was empty, I would get a Verizon signal without having the presence of any alleged CDMA antenna kickstarting /var/wireless/Library plist files. I confirmed all these permutations many times before posting here. Anyway, I deleted the plist files under /var/wireless/Library, deleted the Zeppelin_US.bundle folder, emptied the SIM tray, confirmed the CDMA antenna was disabled (by getting "No Service" in the upper left corner), and continued.
Now, I inserted the SimpleMobile SIM. I discovered through the /var/mobile/Library/Carrier Bundle.bundle symlink that SimpleMobile defaults to Unknown.bundle (under /System/Library/Carrier Bundles/iPhone). (Oddly, with the Zeppelin_US.bundle folder removed, the Verizon factory SIM defaults to Vodafone_nl.bundle.) There was one brief instance where, right after inserting the SimpleMobile SIM, I saw multiple signal bars and the word "T-Mobile" on the upper left corner before the phone locked down with an "Activation required" message, but it happened just once and I have never been able to to duplicate that again. Regardless, I now always get one bar without any service label (no "SimpleMobile" or "T-Mobile"), an "Activation required" message, and receive the same activation error via iTunes I wrote above. (If I activate over Wi-Fi, I receive the same error, too.) Also, oddly I don't see any US T-Mobile bundle under /System/Library/Carrier Bundles/iPhone, just a bunch of foreign T-Mobile bundles. And, the Unknown.bundle folder contains a whole bunch of T-Mobile files in there and the plist file under Unknown.bundle also contains multiple occurences of the string "T-Mobile".
I observed that the international SIM also defaults to the Unknown.bundle folder. At this point I am confused. If the SimpleMobile SIM defaults to Unknown.bundle the same as the international SIM, why do I have to disable the CDMA antenna at all? It seems to me iTunes is transmitting the ICC ID to Apple to decide whether or not to activate the SIM on this phone, so it wouldn't matter what bundle is in use. I know the Gevey SIM is reported to work on a Verizon 4s under iOS 5.1.1, so my logic must be faulty. I'm thinking either Unknown.bundle is somehow identifying my SimpleMobile SIM as a domestic SIM, or the international SIM doesn't really "work", I just have that illusion right now because that SIM gives "No Service", that somehow because the SimpleMobile SIM connects (although I just see one bar), the phone won't activate. I'm thinking the latter because when I insert the international SIM, the phone just reads "No service" and continues working. It doesn't ask me to activate via iTunes or anything.
More than anything, I hope this helps someone. Thanks everyone for your time, especially WhiteSpir1t.
Edit: Maybe I should also add that this phone has never been set-up, registered, backed up, or restored with iTunes. I have just used iTunes to "unlock" and try to activate SIMs.
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