I suppose you had no luck there.

I believe your suggestion is mostly right: after 6 hours, all wallets consider themselves out-of-sync, at least when restarted. I also made a similar hack to try to move things around but unfortunately this time none of my current coin chunks meet the necessary criteria to stake: being still for 1 hour is not enough, although in practice it usually is. There is a flag called "stake-modifier". Your chunks can only stake if there is a block with this flag at least an hour in the future since your chunk was last moved/staked. And this is exactly my problem: most of my chunks are within an hour of that last block, so not eligible at all. I have 2 other chunks that are older than the current last block, just over an hour, but unfortunately the last 2 blocks in the chain (those over an hour for me) do not have the necessary "stake-modifier" flag so I cannot make them stake.
The solution seems to be someone with eligible chunks to try to stake hacking the wallet code and bypassing that 6-hour sync limit..