Are there lenders that would actually let us do this and if so what sort of criteria would need to be met?

That does not yield any sort of return. 

I think its sort of obvious:Whatever sfh your buy for yourselves, you need to get it low enough to pull out enough cash for your next deal. 

This was a live in flip, sort of.... my husband lived there when we met.

How would you approach a seller with this sort of proposition?

Assuming the income generated flows to your schedule E and gets sorted out in the end it may not matter. 

Look for motivated sellers and distressed properties.

What strategies have you used to motivate tenants to quit the lease and move on?

I want to do this all while ensuring my tenants' housing needs are sufficiently met.I'm considering starting with a 5% management fee (and no extra fees), giving the first 3 months of services free as a sort of trial period, and allowing owners to back-out of my services with only a 30-day notice and no extra fees.

I am assuming if you have 20-30% you could put down you would use a lender of some sort.