Even with a VFD, changing direction every 4 seconds is a challenge. That means accelerating in 2 seconds and decelerating in 2 seconds with zero run time at full speed. So let's say you want 2 seconds at full speed, that's a 1second accel/decel time. Yes, a VFD can limit the current, but does so by limiting speed, so your accel time will increase. So you take the motor mass plus the load mass and the accel time to calculate the required torque to make that happen, and because of the constraint on accel time you run into a loop wherein the torque required means the motor mass increases, which increases the torque requirement, which increases the motor mass etc. eventually you will overcome it, but in my experience, the end user is not happy with the motor size you end up with!
As previously mentioned, this is where servos shine, as long as the overall power falls into their range. They have a much better torque to mass ratio.
PS: another aspect of reversing every 4 seconds is going to be the contactors to accomplish this. Most are rated for at best, 1 million operations and with plug reversing, even less. Assuming just 8 hours per day, 20 days per month, you are looking at the contactors lasting 7 months or less. So now you would need to seriously over size the contactors as well. That's actually another good argument for doing this electronically, but I am still in the servo camp if it fits.