I have a similar setup with a remote ts440. HRD does seem to key the rig as well as shacklink does, but my signal isn't getting out enough to test it yet. Rigexpert recommended I try mixw instead of HRD, which seems to be working, especially with digital modes. But again, I can't verify my signal is getting out.
Are you getting any audio dropouts during receive? have you changed the default audio buffer settings? how much of a delay is there when you press PTT to actually keying the rig?
73, N2JAC