If they were to look at a 16-team league with the required 4 OF games, would this suggestion fit the bill?
All 16 teams play each other home and away - 30 games.
League splits into two groups of 8, and each group member plays each other once - 7 games, total of 37 games played.
The two groups then split further, making 4 groups of 4, and each group member plays each other once - 3 games, total of 40 games.
Would potentially make the final games of the season very exciting as it will be teams directly in competition for each other, and would keep the number of games relatively similar to the current system. Also would very likely lead to 4 OF games (unless Rangers are particularly shite one season). Definitely not perfect and the idea of separating the league in 4 parts might be too much for some, but it's just an idea I thought about. Apologies if someone else already thought of this, I would not have been aware of it.