Does anyone know of any programs that will help me get a homeless hospice patient from Colorado to Texas so that I can care for him?

It's a generous thought to want to care for him yourself, in your home.

Start with speaking to his medical team. Find out where he will be sent for hospice.

Then you go there. And visit. Hold his hand.

If he's not incapacitated then he himself should be talking with social workers to figure things out. In this case (and unless you are his Medical Representative, or MPoA) they might not be able to talk to you as his advocate.

If he's been recommended for hospice, I presume he is in bad shape. In this case, I doubt any medical transport company will touch him with a 10-foot pole due to liability and also the duress caused by such a long transport in an ambulance. Even if any service was willing to move him, it is extremely expensive.

As BarbBrooklyn suggested, contact social services for the county where he is currently receiving care if he is now incapacitated. If he's in a hospital, ask to speak to their social worker. It may transpire that the county will acquire guardianship of him which will give them the authority to take care of all his care.

Swan, is he not eligible for a hospice facility, due to the fact that he is unhomed?

Press the social workers at Hospice on this. Can they get him into supportive housing, at least?