Switching between ac-to-ac transformer taps in regulated linear voltage power supply
I've seen that often in linear supplies and they usually did it with relays.
I guess that doing a tap switch with TRIACs or SCRs (essentially the same thing) would be a good solution. It could be a little inconvenient to drive the gates, however, and for 3A probably sticking to relays is better (unless you need to continuosly switch range). An SSR (which is usually a pair of SCRs with some opto circuitry) would be a good compromise.
For you information (for later projects!), these day the common practice is to use a switching converter to pull down from the high voltage rail to something like a couple of volts more than you target voltage and then use a linear to do the final regulation (and less noise/ripple). This is of course more complex but much more efficient.