Ideally the center of the lens would be in the middle of the scene. If you are 72" tall, you might be figuring that you want the top 20" of you in the frame, which would lead to the center being the 62" you say. The center of the lens is often somewhat above the tripod mount, which reduces the height you want by a few inches. You probably want some room above the top of your head, which would lead to a higher camera location. Many tripods I have seen are about 50" high with the legs fully extended but have a central column that can be extended as well, leading to a lens position even higher than 62". Mine, which is intended for things much heavier than an iPhone, puts the platform at 54" with just the legs extended and 70" with the center column as high as it will go. You can also put the tripod on a platform to raise it. You can buy plastic tables that are about 30" high easily. You probably need two to give a large enough surface for the tripod legs.

Because the iPhone focal length is so short, you tend to have the phone very close to the action. This makes the angle more extreme than if you had a longer lens. You can get lenses that lengthen the focal length of the phone, which will reduce the effect if you have the space to set the phone back. I don't do video, but for stills Photoshop has a tool to correct perspective. If you can find one that will do a whole video at once that may help as well.