I'm using MultiBit Classic, and one of my transactions is stuck due to too low fees. The main problem is that I have my change amount blocked until this TX goes through.

I understand that I should wait for some time as it will expire (or be included in some block), but if I'm starting my wallet after this happens, wouldn't it rebroadcast the transaction?

Or even while waiting, should I keep my wallet open, or it will continue to push the TX?

Note that I tried to do a "Reset of chain and transactions" as suggested on their help page, but it seems that this does not remove the transaction from wallet (so I guess the wallet will rebrodcast it). Also, I've uploaded the wallet key into a fresh install of Multibit, but still without luck.