Actually you are fine - I did exactly the same thing with BlueHost and got confused by numbering too but .38 is higher than .4!! I am surprised that support did not figure it out for you - if your php is fine, and you have the correct version assigned to this then it about has to be a missing htaccess file or something like that. I know that you are really close - I have done a few upgrades on BlueHost and run into this a few times - once it was .htaccess, other time client had been doing some random folder copying between versions and a fresh copy of the moodle code fixed it. I would check back again with tech support - maybe you just didn't get the right guy but they have always been super helpful with me.
One thing you can try is to find your php.ini file and turn debugging display on there - that will at least tell you if it is finding the installer...