Have you had a barium swallow? That would show reflux.
Motility should have shown if the little sips of water went down.
Yes, there is non-acid reflux. I had it all the time when I was on PPIs.
However, there is a possibility that your reflux is only triggered by specific foods, as mine is. You can find out if you have sensitivities/intolerances/allergies to specific foods by keeping a careful log/journal of time, what you eat and drink and your reactions an hour or 2 later.
If you find some meals or specific foods, then you have to do challenge testing of the ingredients. For me it wasn't the waffle, it was the maple syrup. It wasn't the hamburger, it was the condiments. It wasn't wheat flour, it was commercially prepared bagels, some breads, frozen products - all of which contain preservatives.
When I collected my list I googled the names of the foods and food sensitivity or allergy. I discovered al my foods were on lists of foods known to have sulfite. Others find they don't tolerate MSG. There are plenty of other allergies (as my allergist calls them).
I was able to control my reflux for a long time by simply reducing my intake of sulfited foods. I only had to go through the operation after being in a wreck that pushed my stomach into my chest. Of course the operation does not stop the food intolerances! I only get tachycardia now from eating the wrong stuff.