Please let me know when you plan to solve a problem, so that I can update the page and we can avoid duplication. I have an integer solution to these problems with a value of 239. That corresponds to 424 in the original formulation. Seymour claims to have obtained 423, but since noone ever saw that solution, I wouldn't bet on it. For all other parameters I use the defaults.
Suggestions are, of course, welcome.
That value has been confirmed by converting it back to a solution to the original seymour set covering problem. We can now use 237.01 as upper cutoff which should speed up the remainder of the search.