I'm not sure what you have to loose by changing the battery yourself, your only concern would be introducing dust into the case and movement. If you change it and it returns to normal you're done.
I doubt if there is a unique TC curve for each watch, that it would be on the volatile memory would probably be even more unlikely. As far as the rate, possibly, but again probably more fixed because it just wouldn't make much sense to put it in the volatile memory.
If after the battery change, the rate requires regulation, contact your regional support center and ask them how to proceed. Like you said the watch is out of warranty, why incur costs and time before you determine you have to?
I doubt if there is a unique TC curve for each watch, that it would be on the volatile memory would probably be even more unlikely. As far as the rate, possibly, but again probably more fixed because it just wouldn't make much sense to put it in the volatile memory.
If after the battery change, the rate requires regulation, contact your regional support center and ask them how to proceed. Like you said the watch is out of warranty, why incur costs and time before you determine you have to?