New Door Rubber too Stiff

Vaseline, no, you don't want to be rotting your new rubber with a petroleum-based product like that. The right product is Sil-Glyde, but it's not going to fix the stiffness you're objecting to. Assuming the new seals are the right profile (not necessarily a valid assumption since you bought from Layson's) and are properly installed, it will take time for the new seals to take a set. You will have to slam the doors extra-hard for a few weeks, and you'll have to slam them a little less hard for a few months, but by and by you won't have to slam them any more. Same goes for installing a new trunk seal. If the doors/trunk are literally unlatchable, then the latches might have been adjusted to compensate for dead (compressed) old seals and you might have to readjust them, but otherwise don't go adjusting the latches before the new seal has taken its set; if you do, the new seals will never seat in and you'll just wind up with doors that don't line up.