How to make him less lonely?

Lately we have this problem with my father-in-law. He has advanced Alzheimer's and is antisocial. He has been a widower for 3 years now and he was dating for a long while until he got very sick in his mind. He cannot socialize because he forgot the details with his old friends. One or two good friends are around if he calls or they would call. He stays at home now. He cannot go to any day program because he does not like people, and he prefers to stay at home instead of a nursing home where he could do some hobby with other people. We cannot be with him all the time as we are not in the same town. The caregivers cannot make him less lonely. He wants a lady companion but he is too sick to date normal people. The only hobby for him is walking - when the weather is bad, he cannot walk and would get stressful about being lonely. We try to be there with him 3 or 4 times a year (the airfare is expensive).
Do you have any suggestion? Should we really try the nursing home? We cannot make him paint or play games at home but maybe a group can make him do it. Would he feel better with the ladies in the home after he gets used to it? Right now he hits on the home care nurse or his lady friends. They are doing a good job play along with him. But no one can be there everyday doing this.

Thanks,

Nina