Difficult call to make!
I know someone who was in a very similar situation.
A good friend of mine, was on checkin for Servisair at NCL, she got wind of the loss of the Easyjet contract and quickly got an application in for Gate Aviation, (who had won the EZY contract) even before the jobs were advertised. Gate offered her a job and she snapped it up, feeling very smug that she had at least secured a job before she was made redundant. Even though Gate was a drop in wages and poorer terms and conditions.
Then came TUPE, and a lot of her colleagues came over to work with her. As a result her colleagues kept their higher wage, and she was left at a loss.
At the end of the day, while she admits she was very hasty in getting out of Servisair, at least she has a job, and in this day and age that counts for a lot.
If I was you, I'd play it safe and accept the part time job, and work your backside off, do all and any overtime going, agree to stop back when needed and make sure that if anyone is going to get a permeant contract it will be you. Look at it this way, a part-timer who goes beyond the call of duty will have a better long term future than a TUPE staff member who does the bare minimum.
Good Luck
RTG!