Just for anyone else who has this problem:
If you have a network, it is not enough to change the php.ini or .htaccess. You also need to alter the settings under Network Admin.
Go to Settings and scroll down to Upload settings. There is a max upload file size section. The default appears to be 1500KB. Set it as high as you want. If you have any limits in the php.ini or .htaccess, it will use which ever value is lower. So, I set the max file size to 20000KB. Under my php.ini the limit is set to 10M, so my uploads are limited to 10M.
Hope this helps anyone else with the same problem.