My experience with naturally-separated eyes matches this story: I can do approximate depth using the out of focus blurs, and I in fact just had my right eye correction tweaked slightly more long-distance vision out of personal preference. Refreshing to hear of someone else enjoying life in that style through voluntary means!

You can order one-eye reading glasses without a prescription online for use on top of contacts, fwiw - might give you a way to correct for closeup work, so long as you have a matched pair of L/0 and 0/R.