Can't restore backup from AT&T iPhone to Verizon iPhone

Question

I have an AT&T iPhone 3Gs and a new Verizon iPhone 4 (different phone numbers). I want to transfer everything from my old phone to my new one, but I haven't been able to restore a backup from one device to the other. The techniques documented in Apple Support article http://support.apple.com/kb/HT2109 did not work for me.
When I first connected the new phone to iTunes to actviate it, I was not given the option to restore from backup as documented in the article. The new phone was activated and then synced, so it picked up apps etc from my old phone, but not the data and settings that can only be restored from a backup.
I tried using the Restore from Backup menu item, but the only backup on the list is the one from the new phone, not the old one (the phones have different names in iTunes). I even tried this with both phones connected to iTunes at the same time, but no luck.
I also tried using iTunes to restore the new phone to its original settings. After I did that, I was given the option to restore from a backup, but once again only the new phone's backup was available on the list.
I'm guessing this is happening because the two phones are from different carriers, but restoring form a backup doesn't overwrite the firmware, so I would think it it's technically possible to move everything from the AT&T phone to the Verizon phone. The support article does say that the instructions are for transferring data to a new phone from the same carrier. but it doesn't explicitly say this can't be done when moving to a new carrier.
I'll eventually be able to get my new phone configured like my new one, but I was hoping I could do this in one shot. Is there some other option for doing this that I'm overlooking?

Answer 1

When I sync photos in iTunes, using the iPhoto option, it won't copy pictures from my phone to iPhoto, it just copies imported photos from the iPhoto library to my phone.
Correct - as designed and intended. iTunes does not handle the import of photos from any digital camera including from the iPhone's Camera Roll. When there are photos/videos in your iPhone's Camera Roll, your iPhone is also detected as a digital camera when connected to your computer.
The only imported photos I have are some that I previously imported from my phone, at which point they were converted from the iPhone format to whatever format iPhoto uses.
What?
iPhoto does not convert ANYTHING when importing photos from a digital camera including when importing photos from the iPhone's Camera Roll. There is not an iPhone format for photos and a iPhoto format for photos. Photos captured by the iPhone are in JPEG format, which is not changed by iPhoto when being imported from the iPhone's Camera Roll. iPhoto supports a number of common/open formats and doesn't change the format of anything. iPhoto is a photo viewer and management application.
I don't want those pictures back on my phone, I want my phone's pictures in iPhoto (actually, I just want them on the new phone).
You don't want the photos that are in your previous iPhone's Camera Roll on your new iPhone? OK. The photos in iPhoto on your Mac that you selected to be transferred to your previous iPhone can be selected to be transferred to your new iPhone under the Photos tab for your new iPhone sync preferences with iTunes. If you want the photos that are in the Camera Roll on your previous iPhone available on your new iPhone, you must import these photos from your previous iPhone's Camera Roll with iPhoto. You can then transfer these photos from iPhoto to your iPhone via the iTunes sync/transfer process. This will be the ONLY way you will get these photos available on your new iPhone since you are unable to transfer the backup for your previous iPhone to your new iPhone.
I can use iPhoto to import everything from my old phone, and then sync my new phone from iPhoto, but the images will get converted twice, from iPhone to computer format on the import, and from computer to iPhone format on the sync. If that's a lossless conversion, I guess that's okay, but I was hoping for something more direct.
Wrong. There is no conversion by iPhoto when importing photos from a digital camera including when importing photos from the iPhone's Camera Roll. When transferring photos from iPhoto on your computer via the iTunes sync/transfer process which is selected under the Photos tab for your iPhone sync preferences with iTunes, the photos are optimized for viewing on your iPhone as part of the iTunes sync/transfer process, which cannot be turned off or changed.
And you don't want these photos optimized for viewing on your iPhone why?
It seems iTunes photo sync is only intended to transfer photos from your computer to your mobile device, not the other way around.
Correct, by design and intention.