First, you really should move away from frequentist statistical testing and use Bayesian statistics instead. It is perfect for such occasions where you want to adjust your beliefs in what UX is best based on empirical data to support your decision. With collecting data you are increasing confidence in your decision rather than trying to meet an arbitrary criterion of a specific p-value.
Second, the “run-in-parallel” approach has a well defined name in experimental design, called a factorial design. The diagram shown is an example of full factorial design in which each level of each factor is combined with each level of all other factors. The advantage of such design is that interactions between factors can be tested as well. If there are good reasons to believe that there are no interactions between the different factors then you could use a partial factorial design that, which has the advantage of having less total combinations of levels while still enabling estimation of effects of individual factors.
Second, the “run-in-parallel” approach has a well defined name in experimental design, called a factorial design. The diagram shown is an example of full factorial design in which each level of each factor is combined with each level of all other factors. The advantage of such design is that interactions between factors can be tested as well. If there are good reasons to believe that there are no interactions between the different factors then you could use a partial factorial design that, which has the advantage of having less total combinations of levels while still enabling estimation of effects of individual factors.