Problems are not solved unless:
- they are both visible to those able to solve them, and,
- a motivation is provided to those able to solve them.
It sounds as though neither condition is yet satisfied.
You need to make the problem visible - whiteboards, post-its etc. showing the work waiting/in progress/delivered are often used. But you have to adapt to individual circumstances - "people overseas" and "management" can't see these through the phone. Maybe an internal webpage?
You need to motivate solving the problem - which only happens when there is a cost to those causing the problems. Apparently deploying untested software doesn't cost them enough to motivate change, so it is hard to know how to make it matter.
At the very least, if you organise things so that you can point to the list of outstanding work then you can say "this will cost you one of those". Or even have a rational discussion about which to do next.