You can't run stroke and match play together really because match play once you can't beat your opponent, you don't play anymore, on the hole or the rest of the holes.
You could do what our league does is play stroke play and you win a point for each hole you beat your opponent and a half point for a halve. If the stroke play is against the field, you can't give putts. Everyone must finish the hole unless you want to do a score cap per hole.