You can do the gearbox calculations yourself, using Vex’s DC Motor Testing Data for the Mini-CIM. Anything over a 2:1ish ratio is going to give you enough torque for straight line runs (if you need to turn, you’ll need to take into account the increased friction from scrub, which would increase the ratio needed). As a rule of thumb, with 4" wheels I would look for a 5:1 or 6:1 reduction on an FRC-weight robot - with smaller wheels and a less weight, you could get by with less.
You can model the robot’s motion a couple of different ways, depending on how you think it’s going to work out. Essentially, it’ll have 3 phases - acceleration, steady speed, and deceleration - while being stationary at each end. On one extreme, you could model it accelerating the entire distance and stopping on a dime(ish). On another, you may accelerate half the time, decelerate the other half. You could accelerate for some period of time, run steady, then decelerate for some period of time.
You can use the JVN Design Calc to run through some options. On the Custom 1-speed Drive tab, you can select the Mini-CIM, set your weight and wheel diameter, and then your gear ratio. The “Drivetrain Adjusted Speed” is a good approximation of the max constant speed you could sustain (does not take into account acceleration/deceleration), and the “pushing” current draw per motor is the most current the motors would take given those settings, if you drive into a wall and stall them. You want to cover 8 m (26.25ft) in 3 seconds, or 8.75ft per second. You can reach that (ignoring acceleration) with a 7:1 (ish, it’s actually a little more, but I’m sticking with nice, round numbers where I can) reduction or less.
The trickier part (for me, at least), is avoiding breaking traction when you start up. You probably won’t be able to give it full speed from the get go, you’ll need a ramp up function to avoid spinning the wheels without moving. I’ll be honest, I don’t know how to model that properly, or figure out what the acceleration/deceleration rate would be. I know some top teams do calculations around it, but for most teams that level of detail is overkill when they can just rely on some basic experience and rules of thumb and still get good performance. Additionally, we’re usually focused on traction impacts in a stall/near-stall condition (pushing against a defensive robot), not in acceleration.
Something else to consider - can you start the robot off to the side a little (a few feet?), and stop past the other side a little? if so, you can use that to soak up some of the acceleration/deceleration, making sure to set up the robot code so it still only shoots within the lines (perhaps using a sensor to detect the lines on the court?) That would make the whole thing a lot easier to manage.
Edit: I haven’t seen the iLite calculator before, I’m going to have to play around with it.