[MarkGritter]

P.S. I tried a couple different suit assignments to get some idea how accurate my sample was (removing the truly awful options).

dddccchh:
-1.16457 3s6s7sJsQs 2d4d6d7c8c 9cThQh 12742
-0.832522 8c9cThJsQh 2d3s4d6d7c 6s7sQs 12742
0.422854 7c8c9cThJs 2d3s4d6d7s 6sQhQs 12742
0.429054 6d7c8c9cTh 2d3s4d6s7s JsQhQs 12742

hhhdddcc:
-1.18815 3s6s7sJsQs 2h4h6h7d8d 9dTcQc 12692
-0.842972 8d9dTcJsQc 2h3s4h6h7d 6s7sQs 12692
0.439332 7d8d9dTcJs 2h3s4h6h7s 6sQcQs 12692
0.450441 6h7d8d9dTc 2h3s4h6s7s JsQcQs 12692

ccddhhcc:
-1.21522 3s6s7sJsQs 2c4c6d7d8h 9hTcQc 12810
-0.874707 8h9hTcJsQc 2c3s4c6d7d 6s7sQs 12810
0.371741 7d8h9hTcJs 2c3s4c6d7s 6sQcQs 12810
0.378454 6d7d8h9hTc 2c3s4c6s7s JsQcQs 12810

hhhhccdd:
-1.16418 3s6s7sJsQs 2h4h6h7h8c 9cTdQd 12669
-0.847186 8c9cTdJsQd 2h3s4h6h7h 6s7sQs 12669
0.399479 7h8c9cTdJs 2h3s4h6h7s 6sQdQs 12669
0.41124 6h7h8c9cTd 2h3s4h6s7s JsQdQs 12669

ccccdddd (Completely live hearts):
-1.22496 3s6s7sJsQs 2c4c6c7c8d 9dTdQd 12602
-0.958261 8d9dTdJsQd 2c3s4c6c7c 6s7sQs 12602
0.302571 7c8d9dTdJs 2c3s4c6c7s 6sQdQs 12602
0.310586 6c7c8d9dTd 2c3s4c6s7s JsQdQs 12602

hhhhcccc (completely live diamonds)
-1.217 3s6s7sJsQs 2h4h6h7h8c 9cTcQc 12894
-0.953389 8c9cTcJsQc 2h3s4h6h7h 6s7sQs 12894
0.318753 7h8c9cTcJs 2h3s4h6h7s 6sQcQs 12894
0.330541 6h7h8c9cTc 2h3s4h6s7s JsQcQs 12894

The choice of suits and different random samples thus seem to impact EV by about 1/10th of a point--- not enough to affect the best choice here.