Yes, Easy Peasy is storing images in the database itself - which is insane.
Uploading a 35MB db is always going to be difficult, especially if one table accounts for most of that size. I’ve never come across BigDump before, but it seems even that failed you.
I hope you have the images in a normal form somewhere.
What I suggest you do is:
1) make a copy of the .sql file
2) open that in a text editor and remove the EPG2_pictures data - everything from
# Dumping data for table `EPG2_pictures`
#
down to the next # comment for the next table.
3) import that (much smaller) file
4) get the site running
5) install a gallery script that doesn’t store images in the database.
If your file is still over 1mb, you may find that it is better to gzip the file before step 3.
I hope this helps.