Do you mean multibit classic or multibit HD? Both of these are no longer supported as the team has abandoned the project, but an old multibit (classic) version has been outdated for more than a year. I remember that I had trouble moving my coins to HD 10 months ago, as it did not  allow you to choose fees manually which meant the transactions were being stuck for days. As you can see the situation doesn't look good since you can't extract the private key and move it to another wallet manually, you have to send the coins to a new address through the outdated multibit client. AFAIK the only way to do it now is to accelerate the transaction.


It seems this is the main problem now. The transaction doesn't get broadcasted at all and it's not visible on blockchain. You'd have to deal with this issue first before even having to worry about a low fee.
I can already tell you that it's going to be a pain to extract your coins from that wallet as it has already been like that in 2016 and now with the rising fees it has become even worse. Try rebroadcasting the transaction until it appears on blockchain.info