If you are going to shy away for ssh then you still have a couple of options which is more steps.
But first remember what was said about extended inserts. You had that option selected when you exported so you would need to export another file and turn off that setting. That may be why bigdump failed.
First option try another export using zip at the bottom. When you import it select the zip file to import do not extract it on your desktop. it will be a much smaller file but the server will pause for a few moments while it is extracting the zip
Other option is when you export the DB break it up into a few download files by selecting a few tables at a time. The big tables will be the posts.
Then import each backup file one at a time.
Or the really slow way is to make a backup from the UBB control panel. It will make a backup file for each of the 65 tables. Then you would need to import 65 times. Once per file.
Whatever option you try make sure your new database is empty, no tables or data because you may have some corrupted tables due to the import failure.
All I can say is on my server I have a limit set to 50mb for importing with phpadmin. Your 30MB DB would take probably 4 or 5 minutes to export or import on my server but I also have a fairly fast upload speed on my ISP service.
