I also have the Hydromax7. For your problem, some things you can try:
1. Take the white insert out (just yank it out, it’s just slotted in, not attached). I think it’s meant to make things more comfortable but I find it a bit of a nuisance. Since removing mine and pumping without it, things seems much better. With the insert in I was getting a non-uniform unit when I finished pumping (the base was noticeably thinner than the mid and upper girth). Since taking it out, not only is my unit uniformly thick, it’s a lot thicker overall (start I was getting a pump to 5.5 inch girth, now it’s more like 6 inches!). The negative is that it does feel a bit more uncomfortable where it’s sucking into the skin around my lower abdomen.
2. Go in hard or semi-hard. What is happening to you is your penis is sitting flaccid in the chamber so when you pump, depending on where it is lying, it might be in contact already with the white plastic. Then when you pump, as what happened with you, your penis will be pumping in contact with the plastic and yeah it’s going to hurt and you won’t be able to pump properly. Key is I) make sure your penis is as central in the bathmate as possible, lessening the chances of it getting impinged by the sides of the chamber and ii) to get your head clear of the insert before you start the main pumping. Once your head is clear you shouldn’t really have any such problems as you mention. No need to use any lube this way as nothing gets pressed or touches. By going in hard or semi, providing you got the right size Bathmate, your head should already be clear of problems.
It should be simple fix, good luck :)