The time it takes to post the running order is not up to Entry Express, it's up to the Hunt Test Secretary (speaking from experience). Once the entries close, a random running order is available for viewing by the HT Sec right away. It's up to them to review the running order, make sure no one is running where they shouldn't (i.e. a judges relative with a different last name, but in the same flight; etc.) and then they hit the button to post the running order.
Since most HT Secretarys also have other priorities (i.e. work, family, etc.

), I've seen it take anywhere from one to five or six days.
As for a 137 dog Master, that seems to be higher than the average test; but some tests tend to draw large numbers, particularly double tests, tests with great grounds, first test of the year in a local area, etc. It also depends on where you are. Here in Oregon, the average seems to be around 80-100 dogs, with some tests as high as 150 this year (probably because the MN is so close).