Your deal doesn't have a good enough loan to value ratio for a typical note buyer discount and for you to come out ahead.I'd not be too concerned about your buyers walking away from an aggressive counter.

The correct way would be to set up an LLC and make them a partner, if the deal is good enough you could use longhorn  investments and get 100% financing. 

I have been able to find some hard money lenders that give me 100% of the purchase price, rehab and closing costs, if the deal is good enough.

I recently bought a property and hired an inspector that my realtor recommended and said he used for his own properties, so I thought that was a good enough reason to hire the inspector myself.

The screening reports aren't quite as robust as when I owned a property management company and used professional software but they are good enough for the receiving applications, screening and collecting rent that I do need.  

I am hesitant to do so because I worry I won't be able to provide a good enough service to tenants.

My Property management deals with tenants (obviously), but we have a good enough relationship where I will send her to potential properties to get me work quotes, and vet the neighborhood.

If this isn't an option then you will need to source and lock up a good enough deal where someone else gets a strong enough return and there is still meat on the bone for you, this could be accomplished with a cash out refi and then split returns after you return your investors initial capital.In either case you need to identify how what you bring to the table helps the person who brings the other pieces (cash, expertise/knowledge, or the deal) so you have a compelling offer to the investor/partner.  

It is important to my wife particularly that if we but a rental house it be good enough (and in a good enough neighborhood) that she'll feel content living in it for a while.Thanks very much!

If they're earning a commission, that should be good enough, but it's very possible they won't see anything for their efforts.