You are proposing an experiment that would be almost impossible to run.

Little if any nutrition research is actually run like a traditional science experiment (i.e. do something specific and observe results). Unfortunately outside of the prison camps on North Korea it is impossible to control the diet (or behaviors) of enough people for long enough to get useful results.

Instead we observe people uncontrolled behavior (almost never directly but through questionnaires) then observe health outcomes (usually not directly) or in this case something (telomere length) believed to be associated with health outcomes. Attempts are then made to adjust for all these potential problems using additional data (usually questionnaires) - usually difficult to say how effective.

These neccesary compromises introduces a whole host of potential problems that have contributed to all the confusion over what is good/bad nutrition. I've given up on having much confidence in medical research until it is repeatedly confirmed in additional studies - which may never happen.

Not at all. I'm wondering what the effect of my family's usual dinner drink is. We have (mostly) unsweetened fruit juice mixed half and half with carbonated water. The only sweetened juices tend to be lemonade or a cranberry mix.

Given that the effects were not seen in diet soda, it's fair to discount the possibility that carbonation plays a role. Since fruit juice has a mild lengthening effect, it might be minimally positive.

The effect were also not seen in sweetened non-carbonated beverages, so it must be some interaction between the sweetening and the carbonation.

I would be careful with words like "must" when there are this many variables involved. It could be fiber, the types of sugar, etc. We do know that carbonation alone isn't causing this and fruit juice doesn't cause this.