Thanks. I emailed the broker website, as I reported here. Don't know if the webmaster replied or just somebody else set up to handle complaints.

If the problem were Safari's scrupulousness, why can I go for several days with no time outs and then be hit for several days with many time outs. Or is Safari's scrupulousness hit and miss?

What about some other possible remedies? Reinstalling 10.9 and then 10.9.1. Or installing an older version of Safari in 10.9.1. Is the latter possible?