Gosh, I must be out of the loop like Bob Chick claims! I haven't heard of Tate or JM presses before. When I looked into what they were I wasn't impressed. You really have to be careful with your elbows. It is way too easy to damage the connective tissue there and if you do your elbows will be sore for the rest of your life. I mean sore when you do heavy lifts without warming up.
Larry Scott is probably the best exercise technician in the world. He wasn't a big guy when he started bodybuilding and had to use his mind to find new methods to get bigger. His programs are still extremely advanced training. He also came to understand the details that are effective in exercise form.
His movement lying face up on a bench is safe and effective. He takes an ezy-curl bar and lowers the weight to below his rib cage. Then he brings the bar near his chest until his elbows are pointing to the ceiling. From there he continues this circle until he fully extends his arms at about eye level. He used slow, circular motions and was using over 225 pounds in the movement. You save your elbows if you do it this way.
Larry liked the lying triceps extensions with elbows placed on a pad. Having the triceps in a stretched position is one of the best movement for the triceps. He specified that the pulley should be 5 feet off the floor for the most effective contractions. Yes, that is exactly how high they need to be. The only improvement I would make is to avoid placing the elbows on the pads. If you do rub the elbows on pads you risk injuring the delicate sheath that covers the elbow connective tissue. So keep your elbows a couple of inches clear of the pads. It helps if you have side pads to prevent your arms from moving to the side. Keep your shoulders and head down and steady. Then reach back as far as you can for each rep. Make sure you fully extend all your reps. I recommend aiming for 15 reps after a thorough warmup of many higher rep sets. By doing 15 reps you tend to get a better pump and you don't cheat as much. If you are supersetting biceps you will find that your reps will drop by the 3rd set to about 10 reps which is okay. Do every set to failure but don't let anyone assist you. If assisted reps are necessary for growth you will need them all the time. Simply do from 6 to 10 sets with the maximum resistance. Don't reduce the resistance. If you want to do more reps then rest a bit more between sets. I superset with biceps to get a bigger pump. Do this routine every 4th day. There is no need to do any other triceps work unless you have plateaued.