Here's an idea: play both Women's and Men's on the same set of days, putting more games on each day.
Tuesday, March 12
Women's Game 1: No. 12 Seed vs. No. 13 Seed, 1 p.m.
Women's Game 2: No. 11 Seed vs. No. 14 Seed, 3:30 p.m.
Men's Game 1: No. 12 Seed vs. No. 13 Seed, 6 p.m.
Men's Game 2: No. 11 Seed vs. No. 14 Seed, 8:30 p.m.
Wednesday, March 13
Women's Game 3: No. 5 Seed vs. Game 1 Winner, 11:30 a.m.
Women's Game 4: No. 8 Seed vs. No. 9 Seed, 2 p.m.
Women's Game 5: No. 7 Seed vs. #10 Seed, 6 p.m.
Women's Game 6: No. 6 Seed vs. Winner Game 2, 8:30 p.m.
Thursday, March 14
Men's Game 3: No. 5 Seed vs. Game 1 Winner, 11:30 a.m.
Men's Game 4: No. 8 Seed vs. No. 9 Seed, 2 p.m.
Men's Game 5: No. 7 Seed vs. #10 Seed, 6 p.m.
Men's Game 6: No. 6 Seed vs. Winner Game 2, 8:30 p.m.
Friday, March 15
Women's Game 7: No. 4 Seed vs. Winner Game 3, 11:30 a.m.
Women's Game 8: No. 1 Seed vs. Winner Game 4, 2 p.m.
Women's Game 9: No. 2 Seed vs. Winner Game 5, 6 p.m.
Women's Game 10: No. 3 Seed vs. Winner Game 6, 8:30 p.m.
Saturday, March 16
Men's Game 7: No. 4 Seed vs. Winner Game 3, 11:30 a.m.
Men's Game 8: No. 1 Seed vs. Winner Game 4, 2 p.m.
Men's Game 9: No. 2 Seed vs. Winner Game 5, 6 p.m.
Men's Game 10: No. 3 Seed vs. Winner Game 6, 8:30 p.m.
Sunday, March 17
Women's Game 11: Winner Game 7 vs. Winner Game 8, 11:30 a.m.
Women's Game 12: Winner Game 9 vs. Winner Game 10, 2 p.m.
Men's Game 11: Winner Game 7 vs. Winner Game 8, 6 p.m.
Men's Game 12: Winner Game 9 vs. Winner Game 10, 8:30 p.m.
Monday, March 18
Women's Game 13: Winner Game 11 vs. Winner Game 12, 5 p.m.
Men's Game 13: Winner Game 11 vs. Winner Game 12, 7:30 p.m.
Note: I'm focusing more on the concept of a combined tournament, not specific days such as finishing on a weekday, and I'm ignoring the dilemma of BYU playing on Sunday. Just trying to show what a combined tournament in one venue could look like.