Pasteurisation would reduce viable cell count in your kombucha which is undesirable.
Refrigeration, as I just recently discovered, only slows the growth of the scoby but it would give you enough time to keep the liquid clear. Given enough time (>3 months in my case), you will see growth at 3C.
Whether it is a single or double ferment, there is really no difference unless your substrate is very different in the second fermentation. The yeast species are responsible for the fizz while bacteria like G.Xylinus is responsible for the formation of the cellulose mat you want to control. I have not yet looked into what makes G.Xylinus thrive, but even in a scoby there has to be some conditions that favour yeasts over bacteria, whether it is a pH threshold or nitrogen or some other micro nutrient.
You might want to experiment with it. What I do notice is that old scoby kept at low temperatures are less capable of producing gas, which suggests that the yeast population is harmed by high acidity or high acidity at low temperature.
G.Xylinus and other bacteria feed on ethanol from yeast to produce acids (primarily acetic and lactic). So, you might want to try a removing the new growth and rebottling without any further sugar addition.
Agitation also prevents mat formation but you will still find sediments and "scum" suspended in the liquid. If that is acceptable, you can just shade the bottles periodically to disrupt the mat.