Thanks guys for the suggestions.  Much appreciated!
I got it working for North American long distance, but not international.
Both local & long distance calls used the same Digit Modification Plan.  So I had to create a new one.
Here's how long distance calls worked today.  They have a bunch of other rules that started with a 9 so I think that's why they broke it up into 8 separate rules like this:
ARS Digit Modification
Digits Dialed | # of Digits to Follow | Term Type | Term Num
912             9                       Route       6
913             9                       Route       6
914             9                       Route       6
915             9                       Route       6
916             9                       Route       6
917             9                       Route       6
918             9                       Route       6
919             9                       Route       6
ARS Routes
Route Num | Routing Medium | Trk Group Num | COR Grp Num | Digit Mod Num | Digit Before Outpulsing
6           TDM Group        1               6             2               ** empty **
ARS Digit Modification Plans
Digit Mod Num | Num Digits to Absorb | Digits to be Inserted | Final Tone
2               1                      {000}1026775            <T02>
Nobody on site was able to explain to me why all those digits were being inserted on every external call -- both local & long distance.  After some trial & error testing, I discovered that the {000} was absolutely required --- without that, any external call failed instantly.  The 7 digit code after that didn't seem to be needed.
Currently this site is using a PRI from the local ILEC.  But their LD is with a third party.  No one remembers how this was setup.  But perhaps the 1026775 is a code going to their LD provider to authorize things?  That sort of makes sense.  But the {000} is still confusing because that should definitely fail if sent to the ILEC's PRI, right?
Anyway, these are the rules I changed/added that got it to work:
ARS Digit Modification
Digits Dialed | # of Digits to Follow | Term Type | Term Num
912XXXXXXXXX    0                       Route       16
913XXXXXXXXX    0                       Route       16
914XXXXXXXXX    0                       Route       16
915XXXXXXXXX    0                       Route       16
916XXXXXXXXX    0                       Route       16
917XXXXXXXXX    0                       Route       16
918XXXXXXXXX    0                       Route       16
919XXXXXXXXX    0                       Route       16
ARS Routes
Route Num | Routing Medium | Trk Group Num | COR Grp Num | Digit Mod Num | Digit Before Outpulsing
16          TDM Group        1               6             4               1
ARS Digit Modification Plans
Digit Mod Num | Num Digits to Absorb | Digits to be Inserted | Final Tone
2               1                      {000}9505551212<T02>
When I had the <T02> in the Final Tone column, it didn't work.  Once I moved it to the "to be inserted" column, then I had success!  I tried using a "W" for the wait as suggested, but a "W" is not allowed in that field.
That gave me the correct sequence of events:
9 <Mitel gives you dial tone>
1 999 555 1212 <local LD access number is dialed> <2nd dial tone> <Mitel outpulses your number>
International calls uses the digit mod rule of 9011 and the Unknown for the # of digits to follow.  Any time I tried using a rule like that, it passed control of the call to the 3rd party LD carrier BEFORE you dialed your LD call.  It looked like this:
9011 <3rd party LD carrier gave you dial tone>
442012345678 <these digits did NOT appear on the Mitel phone, but you heard the DTMF digits>
This is different than their current setup as the LD digits appear on the phone just like in the North American LD dialing.  What am I doing wrong here?
Also, any thoughts on this mysterious 000 that is being inserted on all external calls?  I can't even dial a local number without inserting 000 before the number.  Very weird.