Edit: Thanks to everyone who responded, I've decided to continue the normal recurring gift/recurring gift payment process.
We moved our donations to Fundraise Up, so all recurring gifts process automatically. It seems to me that it's extra work to add a new recurring gift, then add the actual transaction (recurring gift pay cash) and apply it to the recurring gift. Since we don't have to process this in RE, what's the point? Why not just use the Recurring Gift type and post it as I would a cash gift? It won't have any pay-cash gifts. Each month, each gift will be a "Recurring Gift". This keeps us from having to add another attribute or other data points. Is there anything about RE that makes this unfeasable?