I think you might have the regions wrong. There are some distance issues, but the balance just barely works.
Based on your seed list, Tennessee would go to Detroit as that is its closest region. If you flip UNC and Tennesse, UNC would go to detroit as its closer than boston. Arizona goes West, Marquette South and ISU East.
Baylor would be MW, Creighton West (can't be East or South), Kansas East (can't be south) and Kentucky (south)
Illinois South (can't be MW) Duke MW, Alabama East and Auburn W
Big 12 has both Iowa State and Kansas in the East. Not allowed.
SEC is in MW, South, East, West (not allowed
Big 10 is in MW and South
Big East is East, South and West
Pac 12 is West
ACC is West and MW
How to fix Kansas and Iowa State. Can't move Kansas. Creighton can't go to the East due to UConn and Kansas can't go south due to Houston.
Can you move Iowa State? Iowa State would need to go West, meaning Arizona goes East. That really sucks for Arizona. It probably means Iowa State West, Arizona South, but Marquette can't go east. Arizona to the East is probably the only way.
Now MW has Purdue (1), Tennessee (5), Baylor (9) and Duke (14) for a total of 29
East has Uconn (2), Arizona (6), Kansas (11) and Alabama (15) for a total of 34
South has Houston (3), Marquette (7), Kentucky (12) and Illinois (13) for a total of 35.
West has UNC (4), Iowa State (8), Creighton (10) and Auburn (16) for a total of 38
Generally, there should be no more than a gap of 5, so we have a problem. How do you fix it? It is a cluster. You could swap Tennessee, Baylor for ISU, Creighton but that has 2 SEC teams in the West. You swap Arizona and Tennessee and Duke/Alabama
Now MW has Purdue (1), Iowa State (8), Creighton (10) and Alabama (16) for a total of 35
East has Uconn (2), Tennessee(5), Kansas (11) and Duke (14) for a total of 32
South has Houston (3), Marquette (7), Kentucky (12) and Illinois (13) for a total of 35.
West has UNC (4), Arizona (6), Baylor (9) and Auburn (15) for a total of 34
Your MW is Purdue (1), Marquette (7), Baylor (9) and Alabama (16) for a total of 33
Your East has Uconn (2), Iowa State (8), Kentucky (12) and Duke (14) for a total of 36
Your South has Houston (3), Tennessee (5), Creighton (10) and Illinois (13) for a total of 31
Your West has UNC (4), Arizona (6), Kansas (11) and Auburn (15) for a total of 36
Mine has better balance, but yours does save hurt Marquette more than Iowa State. Would the committee like more balance at the expense of benefiting #8 over #7? I don't know.