Thank you very, very much, that site seems to have found the very heart of the problem, and even proposes solutions. Sadly, so far I haven't managed to get it to work.
I replaced both the time stamp value (and later also the starting adventure time stamp value) with 0 (all 5 bytes). I used Psavfix to create valid checksums so the game wouldn't say the save file is corrupt. I tried it on two games and it didn't work. Berries don't grow. The guy at the rocket launch center still tells me that 9999 rocket launches have happened so far so whatever the VBA did to the save file is still not undone.
Also, I looked at the save files of new games I started and played a bit (started with working battery, then saved without battery, than replaced battery and played on, to create the same situation I have with the other games; no VBA to mess things up involved). Their time stamps are all zeros anyways, so I don't know what I could change there to make them work again. Is there some other value I could change the hex code to? I have no idea how the time (and date?) are converted, and if this is explained on the linked website, I didn't understand it.
Can anybody tell me if I did something wrong or could try something else? I feel like I'm so very close to the solution but something keeps me from doing that one thing I still need to do.
If all fails, I guess I'll have to find a GBA flash card somewhere and use the program that the guy wrote to change the clock settings, not the save file time stamp. But even with this, I'm not sure I'd be able to change it to a date that will work with the extreme time stamp(s?) the VBA put onto my saves.
In any case, thanks a lot to everyone so far for investing time and energy into this. I am very, very grateful.