IceDrive isn't unknown, but it is not well known. I think they've been in business for about 6 years. Backups are great, but not worth much if you don't audit them occasionally. 3000 files is a lot OP. Sorry you are in that position. I find it hard to believe tho, that they do not have a complete backup of your files. I mean, 3,2,1 is about a basic of a backup system to impliment. I'd press them harder.
Is this a free account or paid?