I'm no expert on toasters but a bit of basic physics suggests that any device that has to heat up from cold, while the bread is already in place, won't be capable of providing the fast toasting which you're seeking.
I've not got a toaster, simply relying on a good old-fashioned eye-level (gas) grill to produce toast. I always ensure that the grill has been on for several minutes before placing the bread under it, so that it will be really hot. Is there a way that you can get your Breville toaster to pre-heat? (If not, I suggest seeking out a device which offers such a facility. Putting bread into a cold toaster, which then has to warm up, is never going to produce the result that you're seeking).