We've certainly seen that F5 load balancers cause problems just like your seeing when used with LDAP. They just slow things down way too much to be worthwhile.
Do you have any facts/numbers to back this up? I've never seen F5's slow things down noticably. The most common problem load balancers introduce are idle timeout mismatches (where the LB times out and drops an idle connection from it's table that the client and server don't know was dropped, so leave lots of orphaned connections hanging open on both sides, which in turn does cause problems - one of which could be performance). Trivial to fix with proper idle timeout configuration/coordination on the backend server and LB.