Thank you for your feedback!
To achieve the probability spread I wanted, the success number could have been anything except 1 or 6, so I chose 3 since it's a multiple of 6. Using 6 as the "crit" number felt right, and the potential for a crit makes success slightly more likely than a 1 in 6 for each die rolled. I also think it's interesting twist to have players look for a number that isn't just the highest one on the die for success.