Your story sounds like your "fluttering" is not necessarily in your esophagus. Also you might be suffering from food allergies/intolerances.
I used to get a similar feeling quite often. It became worse and was often followed by tachycardia. (Actually tach can feel like fluttering.) My cardiologist and GI doc had no idea, but I started to notice it occurred after eating certain food. All my foods were pretty bland. It could occur even 4 hours after a meal.
I went to an allergist who did some testing and was told I had no food allergies. I went to a highly recommended allergist and she told me when sees this all the time. I was instructed to keep a food log and then when I had identified a meal, I had to do "challenge testing." The challenge consisted of eating a single food - first a tablespoon or so, then wait 20 minutes. If no reaction I ate 2 T, waited, then 4, then 8 and finally 16T.
I came up with a strange list consisting of maple syrup, brown sugar, garlic, pepper, mustard, catsup, most kinds of cookies, anything with corn syrup or corn starch, but not corn itself, gelatin, beet sugar, wine, beer, and lots more. I looked up these words and allergy and found they all contain sulfite. (not sulfate or sulfa!)
On eliminating these "trigger" foods I stopped having reflux and the resulting tachycardia, although I still needed my PPI for a leaky LES. Other people have different "trigger foods."
This problem of esophagus triggering arrhythmias, and vice versa, is not unknown. There are several research papers detailing cardio-esophageal reflex. (That's reflEx, not reflux!)
I would see a cardiologist to see if you are having any problems, although a simple ECG is not going to show anything. Then keep a food log just to see if you notice any connection. At least that doesn't cost anything!
Just because a food is "bland" doesn't mean much if you are sensitive to it! I only figured out that I had a problem after I had a heart attack from eating a bowl of cereal! (also contains sulfite)