Yes, the trick to those, which are far fewer these days than several years ago, was to provide a very professional scope of work with the offer to substantiate why their listing is worth far less than they believe that it is. 

I’ve been wondering the same but haven’t yet taking much time to dive into it.

Another resource to dive into would be your local SSA (Self Storage Association)...each state has one (some better than others). 

Then take a deeper dive into any issues the property has. 

Turn key companies have significant advantages over individuals. 1) They buy further upstream at much better prices, 2) they generally get substantial discounts on materials through economies of scale, 3) are better able to control their labor costs by using the same crews regularly, Ask yourself if you really want to take on all the risk on the off chance that you will really save much money if any at all.

They have to find comparable non-sec 8 rented properties that substantiate the requested rent to determine if it is reasonable.  

This reduces my money in the property, improving the rent return, and lowers my risk substantially.

The thing that makes me question is that HELOCs have a limitation that the cash must be used for substantial renovations, which in this case we wouldn't qualify, but since this is a cash-out re-finance those limits don't apply?

As far as how to structure, dive into what type of deal is this.

Usually, the landlord has set a competitive price based on local market rental pricing; you can try, but chances are there won't be a substantial change even if you're able to negotiate them down (and if there is, kudos to you for being able to get that done!!).