Would going on a liquid diet help with reflux if regular dietary restrictions aren't sufficient?

Not a long term plan. You're right--the stomach empties liquids faster than solids, so there is less to "reflux" on a liquid diet. Seriously, how long do you think you can stay on a liquid diet, nor is it wise from a nutritional perspective in an otherwise normally-functioning gut. If gerd has been confirmed (dysmotility, heart, chest, lung, other diseases considered & ruled out) why not try an acid-blocker in low dose?
Don't do it. Although a liquid diet would increase the rate of gastric emptying, which would in turn may decrease the amount of food in the stomach causing reflux, the underlying cause of your reflux would not be fixed. Furthermore, a liquid diet as not a healthy long term solution and i would not recommend this.