You’ve got a great career, likely with some flexibility in scheduling if you can make that happen….my wife supported me as an RN starting out in this self employed world my first year of leaving traditional employment behind me.  

We have a non conforming loan program for this with no job/employment/income (not even stated) however some states will not allow it like WA state for instance.What state are you in?

Is their employment (or way of paying rent) stable?

There's a few different strategies you could employ to free up your capital (bridge loan to re-fi). 

Dover is a fantastic market right now benefiting from the proximity to Portsmouth, new high school and local employers.

A little background first: wife and I have good jobs as professionals; live in the Los Angeles area; I have a CA real estate broker's license; Wife is w-2; I am self-employed; had a couple condos years ago, but did not enjoy the property management part; have been successfully investing in the stock market for a few years (even this year!)

As being self employed most of my life I had to get creative some times and hustle.

All contracts, options, or other devices not based upon a substantial consideration, or that are otherwise employed to permit an unlicensed person to sell, lease, or let real estate, the beneficial title to which has not, in good faith, passed to such party for a substantial consideration, are hereby declared void and ineffective in all cases, suits, or proceedings had or taken under this chapter; however, this section shall not apply to irrevocable gifts, to unconditional contracts to purchase, or to options based upon a substantial consideration actually paid and not subject to any agreements to return or right of return reserved.

If they are self employed, I woulds ask to see at least 3 years worth tax returns and 4-6  months of bank statements.

I verify employment by looking up the number of the applicant's employer myself and calling the company to ask for the supervisor.