My elderly father is severely overweight and bedridden.

Call hospice and tell them that you need help. The two most important things here are: 1. His pain management; you can't provide good palliative care and ease his pain if you can't keep him clean. 2. You can't risk physical injury to yourself. This call might meant he's transferred to a hospital or nursing home but he'll get the best palliative care possible. There is no shame in asking for help and no shame in telling them you can't move him due to physical limits or fear of causing him pain. You can still be with him, you can still be loving and supportive, you're just doing it in a place with the personnel, the training and the equipment to do the physical work.