Before giving up on your place, I'd take Daleth's friend's advice, all of which looks rock-solid.
When I was searching for a similar situation, I contacted a couple of Realtors who had handled recent sales for friends of mine. Sure enough, one of them came up with a fellow agent who had a luxury home with a full guest suite. Seems a relative was pushing to move in and they did not want her there, so they rented to me. We are still friends and she has sold me three houses since.
If I looking today, I'd create a rental resume, spiff myself up and call on as many Realtors holding open houses I could find in the areas I wanted to live. You may have better luck alone or with just one roommate, as a unit large enough to house three adults may be less likely to be lurking in the shadows.
Side note: My FIL owned an 8-unit apt. bldg. in Berkeley, which he purchased before their Rent Control laws were enacted. He hated the RC laws and the fees he was required to pay when a unit turned over, so he never filled any vacancies. He finally ended up with just one tenant in the building, who stayed there until he died. In a sweet twist of fate, the last tenant had no heirs, and bequeathed his entire estate to my in-laws.