i really hope this will not happen.
you are very dedicated to your work and i am sure your costumers will understand it. try to bring the news coverd in a gift box...
like, tell your costumers that your company has grown and thats why you need to switch to new servers that work with a different "payment company" and because they are VIP costumers they will get a nice gift bla bla... and at the end tell them that the subscription will be changed to a different peckage that includes much more but cost the same and they need to switch for that to patreon... but also make clear that they dont need to be worry there will not be double charge.
there is no reason for them not to agree if they need your service and are happy with it. it happens to us all many many times that companies change policies or ask to put credit card again because of a change in their company.
i don't think you need to be worry just think carefully the strategy how to bring those news to your costumers. at the end nothing really changes only the payment processor. you stay the same, service stay the same, costumer stay the same.
good luck