My suggestion for golden tickets would be to use them as ongoing reward tokens for using your Monzo account in a way that’s desirable to Monzo, rather than as one-off entry rewards.
For example,
Make x contactless transactions in a month - get a golden ticket.
Make x direct debits in a month - get a golden ticket.
Have your salary paid directly into Monzo in a particular month - get a golden ticket.
Transfer money to your account via debit card - lose your golden tickets for that month.
At the end of each month each of your golden tickets act as tokens to access some kind of reward scheme. This doesn’t need to be particularly costly to Monzo. It could be something like entries into a monthly cash lottery or it could be money-off vouchers at partner merchants (I assume here the cost would be borne mainly by the partner merchant who would see an affiliation with Monzo as a way of promoting their products).
I think this would attract people to sign up (as they would be getting rewards for just using a bank account), would encourage ongoing use, and wouldn’t be expensive to Monzo.