I suspect you are right to think that this is acrokeratosis paraneoplastica and polymyositis related to an as yet undiagnosed internal malignancy. The involvement of the knees, elbows and glans penis does sound more like garden variety psoriasis, however, the 80-pound involuntary weight loss makes it a malignancy until proven otherwise to me. This is a classic presentation for HIV associated psorisis.
Diagnosis is dermatomyositis.
I have seen the exact same situation in a patient with metastatic melanoma. Psoriasiform eruption does occur with dermatomyositis, especially scaling of the scalp. In response I would favor Basex syndrome and look hard to find a malignancy. A little zinc deficiency coupled with other dietary deficiencies might explain this. Multivitamins and Sustacal for a therapeutic start.