I'd swap that. Charge the $10 immediately, then bundle the pro-rated refund of the half of the month you missed into the first month's subscription charge.
Yeah exactly. This is the extremely simple solution which closes all loopholes and avoids a horrific mess of new fees.
I'd like to take Patreon in good faith here and assume they've just blundered into a huge mistake which benefits nobody except for the payment processors. If so, they should be correcting course in the next few days. But until that happens, I remain skeptical.