Power issues with mixed models
Could you maybe check in simulation?
I'm a huge fan of the workflow described here:
https://betanalpha.github.io/assets/case_studies/principled_bayesian_workflow.html

You are asking question #3 of 4, the "inferential adequacy" one, right? Can you run some simulations with varying 'true stimulus-set gap' and just see how big a gap you can tolerate with your design?

You don't need to know the true data generating process to do this, generating responses from the model tells you something useful about the model+design setup, in this workflow reality has to wait until question #4. Also an important question, but checking against reality comes after passing the tests you're talking about.

Although you don't need to know how people actually come up with their responses, you do need to be Bayesian enough to be comfortable putting priors on all the parameters. If it's important to convince a colleague with the results, might be worth checking that's not a dealbreaker for them!