You say YOU are planning on becoming a catechumen soon, but what does the priest of the parish where you’ve been attending the most say about that? You might think you’re ready, but the priest has different ideas.
Where have you been attending? I know multiple people who’ve gone between the Antiochians and the OCA as catechumens, for example, with little trouble.
As to the question of if you would have to restart the catechumenate from the beginning, it really depends on the priest of the parish where you’re moving. The priest will talk to you, find out what sort of instruction you’ve had, possibly even talk to the priest of the parish you’re leaving.
Do you know where you’ll be moving? If so, talk to the priest there NOW (or email him). Talk to the priest where you’ve been attending, as well. You never know, the two priests might know each other and that can help smooth things along.