Each time the dishwasher runs, water flows out of the air gap onto the counter. I noticed that the top of the smaller interior pipe (cut on an angle) is so tall it makes contact with the cap of the air gap; that is interior plastic cap. I wonder if this could be presenting the problem? I recently had the pipes cleared under the sink so I feel I have eliminated that possible cause.

I am no fan of counter to air gaps. The plumbers in my area will not install them.
Here's a suggestion. Remove the old air gap and replace it with a soap dispenser and run a hi-loop air gap. (see image) Although web have had countless complaints on counter top air gaps we have yet to receive a single complaint on a high loop. Just remember to loop the hose as high as it will go and secure it with a pipe strap. Good luck, Tom