Hypasus do you mean multiplexing the inputs ? The multiplexer capelet does just that. Schematics are here https://github.com/BelaPlatform/bela-hardware/tree/master/capelets/multiplexer/mux_capelet_A2 .
I have no idea what current is required by your LCD, but 3A seems a bit overkill for this application... Rather, unless you are using an LDO regulator, I would go for 15V AC transformer if you plan to use ±12V DC supply rails. I used to have troubles with 12V AC to be used for 12V DC supply rails because of fluctuations in the power grid in my area. Power outlets are normally rated ±10%.. When I had this issue, my synth would be unstable at random times of the day, or depending on the location, depending to what the mains voltage was in the area at the time.
Using two 1n4007 in a bridge rectifier configuration, you get a combined voltage drop of about 1.4V, so you get an unregulated DC voltage of
(12V - 1.4V)*sqrt(2) = 15 V
But if your mains voltage is 10% below the nominal value, you effectively get 13.5V. Considering the LM78xx/LM79xx series has a dropout of about 2V, an LM7x12 would not be capable of producing a regulated 12V output from an unregulated 13.5V input. 15V AC gives you a better safety margin on this. Again, your power requirements should not be huge and you should be able to comfortably fit in the 500mA provided by standard LM78xx series. Otherwise, I believe there must be a high-current version of these regulators