If you can remove the door for the day to paint it that should help. We found that any oil base paint, but especially the marine grade oil base paint, tended to drip - or maybe we just weren’t used to oil based paint any more. If you can paint the door while it’s flat that will be easier. I do agree that marine grade paint/stain/varnish is worth the extra effort, especially since your door gets exposed to rain.
I love keypad locks. There are more expensive ones than Schlage, but I’ve been happy with their quality. We do not use the Wi-Fi type as I’ve read they can be too easily compromised. Multiple codes are nice if you need to let in someone when you’re not at home or are bedridden. You may have better luck finding deadbolt keypad locks with online stores than a local store.