[mshafer1]

The experience that I had with mecanum (while on 3288) was not positive. Keep in mind that mecanum relies on counter angled rolers to produce a net vector to the side. This means that when you wish to stop (especially moving forward or backwards) that there is a free roller on the ground for each wheel yielding the freedom for the body in motion (the robot) to continue in its path until friction wins out. Granted, the counter angle of the rollers helps lower this a little bit, but the more weight your robot is carrying, the more kinetic energy there is, and the farther the robot will drift. It may be possible to use the accelerometer and to counter this effect from software, although likely difficult.
Slide or H-drive is basically tank drive with extra functionality, and the cross wheel will need to be designed for the extra weight, but the drift effects from extra weight will be significantly less noticeable due to the energy working on the entire drive chain and the motor.
An alternative solution to either of these is to have the robot built early enough that your driver has practice and knows how it will behave.