Didn't read the whole thread but I read that the house was built in 95.
In Canada since the late 70's all kitchen receptacles have to be individual circuits.
In other words every double counter plug is run with 14/3 wire which has a white black and red wire.
The neutral goes to the side with the silver screws.
On the opposite side which has gold screws you cut the jumper bar between the 2 screws and you place the black wire on one screw and the red wire on the other.
At the panel end the white goes to the neutral bar the red to one breaker and the black to another.
This way each plug has its own 15 A circuit.
Circuits are designed to run at 80% so a 15 A circuit should only be run at 12 A.
Remeber that Watts/Volts = Amps
14 Ga wire is good for a 15 A circuit.
12 Ga wire is good for a 20 A circuit.
ETA: If your house is properly wired and somebody added the dishwasher after the fact you can remove the double counter plug and replace it with a single counter plug and use the second circuit for the dishwasher.
NEVER RUN A 20 A BREAKER ON 14 GA WIRE UNLESS YOU ARE INDEPENDENTLY WEALTHY AND CAN AFFORD TO PAY FOR REBUILDING YOUR HOUSE AFTER A FIRE BECAUSE YOUR INSURANCE COMPANY WON'T COVER YOU.