Sounds vaguely similar to the issue I had with SOAS after completing my CertHE there, as due to an error they never actually awarded the qualification. Took months to sort out, and only really got sorted because in the end I had to constantly chase them up once or twice a week (in person!) to get them to make progress on it...
While normally when contacting academics I recommend people not expect immediate responses and accept a couple weeks response will be normal, for contacting uni administrations such as in this case I actually suggest the other route and be really on the ball with it, continually keep in contact for regular updates and ask for them to set clear expectations on when it will be done and then hold them to those.
You may also need to see about going in person to their registry office/student records office to have a robust conversation about your requirements for this and the need for them to sort it out (as ultimately if they failed to properly calculate or award your qualification at the time that would be an error on their part).
In the meantime you may want to see if the other uni will accept the transcript either in lieu of the degree certificate or on a temporary basis while you sort this out.