Re: Irimi/too slow problem
Take a 50 or 75 lb heavy bag and suspend it from the ceiling. Make sure the anchor is very very solid. The anchor into the ceiling should be metal and the rope should be connected to the anchor using a carabiner rather than just the rope or the rope will break too soon.
Hang the bag so it is at your body height and approximates a partner with whom you can practice.
Start the bag swinging in a full, slow revolution swing. Use the bag as your partner as you practice your Irimi, Tenkan, Tenkai, and Tenshin movements. As the swing shortens and the revolutions are faster, you will need to start moving faster and faster. The higher you hang the bag and longer the rope, the slower the revolutions will be. The slower revolutions allow you to recover more slowly for the next attack of the killer heavy bag. If you want to make it interesting, put short sharp spikes into the bag to make any hits on your body hurt and motivate you to not be hit. I sometimes use a big log that has spikes in it. It allows me to simulate an attacker with tanto and allows me to hit it full force to practice atemi. Be careful you don't hit any of the tanto sticking out of the log. I poked a hole in my hand that way once. It made me much more accurate in my atemi from then on.
You can use it to play jokes on your students as well. I replaced the usual log with another old rotten one and when the student hit it, the log exploded. He thought he was real tough and apologized profusely for busting my log. It gave him a lot of needed confidence though. He wasn't trying to dodge the log so much after that and allowed for a much smaller safety margin so that he was much faster and more direct in the entry. So, I guess it wasn't so much a joke as a training aid.
In the end, you should be able to do a fast flowing set of movements without break as the bag continues to attack you. You should be able to do the movements until the bag is completely stopped. After that, shorten the rope and start doing faster and faster movements until the exercise becomes almost anaerobic.
It is a lot of fun and I can keep doing this exercise and its derivations for hours. I also use it for practicing knife fighting, practicing atemi including keri practice, practice for my kendo waza, and for jo practice. Just use a 1/2 inch auger and drill out a hole in the log to allow you to replace the spike with sticks of different lengths. Use the length of the rope to change speed of attack.