In fact, buying something that needs a bit of work may allow me to pay cash, renovate, and then refinance and pull out a large portion of the capital I have invested. 

If you buy a 4-Plex and decided  to pull a permit for one Unit to start your renovation project and not the other 3 can the building inspector (plumbing, electric) mandate that you show the other 3 units during the first unit inspection ? 

It needs some renovation, is currently worth about $215,000 as it sits and about $285,000 after $40k of renovation based on comps.

If they are a real Turnkey company, they should own, renovate, and manage their property all in house.

Recently purchased a duplex in Lakewood, OH and am about halfway through renovating both units.

I just shake my head...I have had to cancel two deals on single family homes that I was going to live in while renovating because of the same issue.  

., if you can switch to a 203k or a conventional renovation loan (is it Homestyle?)

I would look at some there, look at some out-of-state, and then in both locations look at both commercial larger buildings and smaller residential buildings.

I am purchasing at $150k cash and will need to do some cosmetic renovation as well as new roof and hvac system.

I could see this working if you tried it this way:-buy a very distressed property that somehow still qualifies as "livable"-perform a live-in-flip style operation, minus the flip at the end-do a cash out refi based on the higher value after renovationYou'll have to make sure your cost of renovations are much lower than the equity built.