It's been covered by the other responses, and I'll agree, mixing medal and team match play just doesn't work. Maybe you can consider two distinctly different aspects of the trip. Two days team and two days individual?
FWIW, I host a 20 person Ryder Cup event each year with friends. One day. Three formats. Thirty six holes. So, you can definitely made a Ryder Cup event work well with only 2 rounds of golf and offer a different, individual focus to the remaining rounds.
Here is how we run our RC event. We learn something each year and almost find ways to improve: https://www.eastbayrydercup.com/
It's been covered by the other responses, and I'll agree, mixing medal and team match play just doesn't work. Maybe you can consider two distinctly different aspects of the trip. Two days team and two days individual? FWIW, I host a 20 person Ryder Cup event each year with friends. One day. Three formats. Thirty six holes. So, you can definitely made a Ryder Cup event work well with only 2 rounds of golf and offer a different, individual focus to the remaining rounds. Here is how we run our RC event. We learn something each year and almost find ways to improve: https://www.eastbayrydercup.com/