Bouncing an idea based on @BMU:
Everyone who would be in or currently tiebreaking gets tossed into a special round 10 draw. To create even groups of 4, 0 to 3 players below them would be drawn/meme'd in to this pool such that the total number is divisible by 4.
Just like Bowen proposed, run seeds 1, X+1, 2X+1, 3X+1 / 2, X+2, 2X+2, 3X+2 / etc.
(X = [# of players in pool]/4)
Everyone else (or for the next Y points away from the tiebreak) gets put into the classic "closest 4" groupings.
This prevents issues with lucking into/out of the top 40 round due to seeding and creates some interesting mechanics around the bye positions. If there's 48 for example, some groups may incorporate players of all desires (5/17/29/41: "I want double bye"/"I want bye"/"I want security"/"Let me in")