Hi, after lots of years on the various medications they just do not work as well, so "freezing" and longer more aggressive "off" periods do become part of the pattern. The more aggressive stiffness during an "off" period makes a person more vulnerable to injury if they do try to shift themselves or if someone else tries to help them. So the physio could be a source of good advice.
My husband and I spend time finding ways to "trick" his PD symptoms, like others have described above ( kicking a ball, singing or whistling, dancing or walking backwards). For stiffness we find that gentle massage works, not just in the regular way that massage can unknot tense muscles, we think that it triggers a different part of the nervous system and can therefore deactivate the nerves responsible for the spasm. Just the act of interacting, talking about it and trying different things also gives us a way forwards and gives him a constructive focus which calms him down and helps to get him through the fog of anxiety. If your dad is hallucinating then that will be stirring up big emotions of fear, and maybe defensiveness and hopelessness, which is why they have had such an undermining effect on his abilities to cope. If you feel comfortable about doing it you could ask the physio for advice on how you could use touch/massage to ease his physical and psychological pain; we all need physical contact, words alone are not enough.
And I just want to ask you who is around to help and support you? You need others around, whether is friends, volunteers or paid care staff; you can't carry this all on your own. Don't forget your own needs in all this.