Whenever I've done it, I've found it helpful to not even breathe.
I think some people use Rodico (a cleaning putty used by watchmakers) to hold them in place (leaves no residue). I've only ever just gingerly put them where they needed to go and kept doing it until they all stayed long enough to get it together.
That chewed up blade looks pretty bad. You'll want to sand that damaged part as smooth as possible and I think it's still likely it'll mess up again.