I don't think it's possible to charge existing customers from Stripe's admin right now.

I don't think this is correct. Stripe (and the Stripe Admin UI) gives you enormous power to charge/upgrade/downgrade/enroll existing customers.

I'm curious, why did you choose to implement your own subscriptions, instead of utilizing Stripe's? This is a much more appealing option if its a clean integration that simply leverages all of Stripe's features (MoonClerk does this well).