If I were your tenant I may be pissed if someone came in to clean my place on a regular bases or very happy to have a free house keeper.I may not want a stranger messing around my stuff or not appreciate the inconvieance of having to be there to supervise a stranger.If I were a single guy I would never clean and simply let your staff do it all but I can be absolutely certain my wife would never allow someone in to clean up behind her.If you decide to provide it advertise your units as having free house keeping included.

Do I be as direct as possible and let them know I'm beginning a real estate business and I was wondering if they'd be interested in selling their house, or try to build some kind of rapport with a total stranger?  

If you are not comfortable talking to strangers on the phone and in person it could take years.

The lawyer has a fiduciary duty to his client, not to you some stranger. 

Strangers don't invest in strangers, they invest in friends they trust.

@Jessica ZolotorofeWhile I appreciate your time and effort here as I am not sure if I can be this patient with a total stranger, I agree we should stop this discussion here as things just seem so different...I am very familiar with what you mean by % of interest, as opposed to the whole building...

You'll be surprised at the number of people that will say, I might be interested, tell me more.My sister once found private money by talking to a stranger on an airplane.

I am surprised some stranger will even disclose she has 100 properties, oil wells. 

Even then, partnering with strangers is rarely recommended. 

Or rent it to strangers for a year or so and then gift it to the kids.