Re "cheap" change management solution

The most important bit for compliance is getting the processes and
authorities right.

Not about "who actually promotes stuff from X to Y".

The important things to sort out is:

What is the reason for this change and who approved the work.
Who tested and certified that the change gave the expected result (and no
surprises on the sidelines).

Quite a lot can be achieved in documenting changes and creative use of Audit
Journal.

If you implement a change management tool without having the change process
rules agreed upon no tool can really help imho.