Delighted to see the Ryder in Italy, and it's good for the game. For all its flaws, Golf is quite a good game for showing the beauty and grandeur of a countryside. And that suits Italy fine!
The excitement of even the early stages of Ryder cup, compared to almost any other golf competition, also reinforces my view that we desperately need to bring a matchplay element into the Olympics.
There are ways you could do it in singles, but the better idea may be to introduce a high-speed fourball format (say over 9 holes) for men's and women's pairs, and perhaps a foursomes for mixed...
9 hole format - every hole is worth 2 points, so W2, Draw/share hole 1, lose 0 - within the match, 10 pts wins the match - if you win the last hole while Dormi, you'll get 11 pts, and still win. If it's 9 pts each after 9, golden point is simple 1 shot nearest the pin tie breaker on nearest part 3...
You could have 4 groups of 4 pairs, doing 2 9 hole group matches back to back in the morning (1-9 and 10-18), and the third that afternoon. Top 2 in each group to QF next morning, again 9 holes, semi finals, again 9 holes, medal match that afternoon 18 holes (19 points to win, or score on the traditional method)
In group, h-2-h is tiebreaker, if three pairs tie on 4 points (2wins, 1 loss) then goes to score difference (10-6, 10-4, 9-10* would beat 10-8, 4-10, 10-8).
Whole thing could be done in two days. Following two days do the foursomes as plain knockout, no groups, again on 9 hole format.
So, basically, singles on strokeplay, pairs on matchplay, with pairs seedings based on final totals in strokeplay. Strokeplay 72 holes no cut, matchplay - "powerplay" 9-hole format.