You are fabulous. I checked the phpinfo() and sure enough, the shopping cart that doesn't have the PHPSESSID has 5.5.2 with:
session.use_trans_sid set to 0
while the shopping cart that does have the PHPSESSID has 4.4.7 with:
session.use_trans_sid set to "On"
Oh man, this is great news. This means that the DreamHost support guy made an error in a)not asking me which version of PHP I was having the issue with, and b)he might also be wrong in telling me that the method you're suggesting won't work (when the PHP manual seems to indicate it would work)
Which method would work on 4.4.7 on CGI - the .htaccess or using ini_set('session.use_trans_sid', 0); ?