I would not get at least 1 amp from the 12 volt side. Why cant't I use the same single 3 lead secondary? I get 7 volts from the middle lead and outside lead, and 14 volts from the two outside lead. It supplies at least 3 amps.
No. The 7-0-7 winding will make what you need for the ±5V, but not what you need for the ±12 V.
To make your regulators work you need:
● at least +7V from ground into the LM7805
● at least -7V from ground into the LM7905
● at least +14V from ground into the LM7812
● at least -14V from ground into the LM7912
All of your measurements need to be made
from ground, not differentially.
If you can't get the current you want from the 20-0-20 secondary, then I'm afraid that the transformer that you have may not be what you need to match your wants. Also, after going through rectification, filtering and regulation, the DC current will be significantly less than the AC secondary rating of the transformer.
PS. Connecting only to the center tap of a winding does nothing, since no current can flow. It's like connecting to one terminal of a battery.