Hershel,
Well the two obvious things you can look at, which I am sure that Mitel has already, is your Audio Frames/IP Packet and your Minimum Playback Time.
The higher each one is the greater the latency, but the more jitter is reduced. To find these look under your SIP trunk programming for the Call Configuration it uses and see what they are set at. If they are default then most likely that is not your issue.
Another thing to look at is whether or not their equipment is doing deep packet or SIP inspections as those will slow down the entire traffic into and possibly out of the network.
Get a wireshark capture when this is going on and you will see how long the turn around is on your side. Unfortunately you won't be able to see what is happening on the other side unless that company is willing to work with you and provide those.
Thanks,
TE