My iPhone isn't directing me properly to messages since I moved to the UK from Canada. When I receive a new iMessage it opens a 'new message' thread to their number in a UK format rather than directing me to the established thread under their name.

Question

I moved to the UK a week ago and popped a new SIM in my unlocked iPhone 4 (all the latest software installed, 6.1.3, though I see in the drop-down below that there's a .4?  My phone says it is up to date anyway).  Since then, I have done a lot of texting to people back home in Canada.  Of course, for economical reasons, I am using iMessage.  When I'm talking to them, if I have messages open, and my screen hasn't gone to sleep, then I'm fine. But if the screen goes to sleep or I'm doing something else and I try to reply by way of any sort of notification where the phone redirects me to the message (when I tap a banner or unlock while an alert is showing), instead of sending me to where I can reply, it starts a whole new text message with the person's phone number in a UK format instead of their contact name.  Their message is in the iMessage conversation history where it belongs, but I can't read it in full until I cancel the 'New Message' and open their conversation in the Messages list.
So far, I have tried:
-Simple things like restarting my phone, resetting it, etc.
-Changing the format of their number to include country code, to not include country code, to have the plus, to not have it, etc.
-Changing where my messages come from, be it my phone number or my iCloud, etc.
-Updating iCloud to make sure it knows I'm in the UK.
-Resetting everything in the reset menu one at a time (I had hopes for settings and the Location & Privacy ones, but no). 
-Erasing all content and settings and restoring my phone from a backup.
I've pretty much messed with every setting, but please let me know any suggestions you have, I may have missed one.
It does seem as if the format of my contacts has something to do with it, because I don't get a notification at all if I change the setting "Show iMessage Alerts From" to contacts only.  The iMessage goes through to the iMessage conversation, but the alerts I get seem to think it's a text message as it comes through with a sample of the message in the alert under their phone number.  It's only when I try to reply through an alert that it screws up.  I know this may seem small but it's driving me nuts, especially because I don't memorize people's phone numbers anymore so I don't know who sent the message until I exit the new message and look it up!
Please help me before I go mad!

Answer 1

I moved to the UK a week ago and popped a new SIM in my unlocked iPhone 4 (all the latest software installed, 6.1.3, though I see in the drop-down below that there's a .4?  My phone says it is up to date anyway).  Since then, I have done a lot of texting to people back home in Canada.  Of course, for economical reasons, I am using iMessage.  When I'm talking to them, if I have messages open, and my screen hasn't gone to sleep, then I'm fine. But if the screen goes to sleep or I'm doing something else and I try to reply by way of any sort of notification where the phone redirects me to the message (when I tap a banner or unlock while an alert is showing), instead of sending me to where I can reply, it starts a whole new text message with the person's phone number in a UK format instead of their contact name.  Their message is in the iMessage conversation history where it belongs, but I can't read it in full until I cancel the 'New Message' and open their conversation in the Messages list.
So far, I have tried:
-Simple things like restarting my phone, resetting it, etc.
-Changing the format of their number to include country code, to not include country code, to have the plus, to not have it, etc.
-Changing where my messages come from, be it my phone number or my iCloud, etc.
-Updating iCloud to make sure it knows I'm in the UK.
-Resetting everything in the reset menu one at a time (I had hopes for settings and the Location & Privacy ones, but no). 
-Erasing all content and settings and restoring my phone from a backup.
I've pretty much messed with every setting, but please let me know any suggestions you have, I may have missed one.
It does seem as if the format of my contacts has something to do with it, because I don't get a notification at all if I change the setting "Show iMessage Alerts From" to contacts only.  The iMessage goes through to the iMessage conversation, but the alerts I get seem to think it's a text message as it comes through with a sample of the message in the alert under their phone number.  It's only when I try to reply through an alert that it screws up.  I know this may seem small but it's driving me nuts, especially because I don't memorize people's phone numbers anymore so I don't know who sent the message until I exit the new message and look it up!
Please help me before I go mad!