As you say, dump and import can take forever. A much better option is to use xtrabackup, which will do a restore about as fast as it can copy the files into place. I blogged about it a while ago. I find it's a perfect way of setting up slaves, really quick and easy. The backups take a long time, but restores are really fast. I also strongly recommend you use pigz instead of gzip if you're compressing your backups - it easily made a factor of 4 difference to my backup times.
If you can arrange to stop both slaves at the same time (so they are both pointing at the same log and position on db1), for example by stopping DB1 momentarily, then you can safely repoint BAK at DB2 using its master info with no need to do a lengthy restore. As troyengel says, most important is that you need log-slave-updates on to do the relaying, otherwise only statements that originate on DB2 will get sent to BAK.
I'd also recommend you set DB2 to read-only. This won't affect replication, but is safer as you won't end up with data on DB2 and BAK that's not on DB1.