This is not a Fannie Mae or Freddie Mac product, so the odds are it won't be main stream.

With a rehab budget under 35K, you could look into a streamline renovation loan product.  

Traditional mortgages are what you typically think of with a 30 year fixed rate loan or similar product.  

It would fall under a commercial lending product and most commercial lenders to not want homes in their portfolio.

Lenders will then easily be able to review your finances and provide you with estimated numbers on different products like FHA vs Conventional. 

The only drawbacks right now is that lenders are not really being as aggressive on ARM products as they used to be. 

You can try and contact some local banks and see what loan products they offer.

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Id suggest that since you changed loan products, presumably without the permission of the seller, that you pay to get these items repaired so that you close and do not default on the contract.

Primary residence loans that are not the usual product backed by the government are called "non qualified mortgages" aka non-qm.non-qm providers can be more creative like using bank statements instead of pay stubs, but I can't think of anyone that does not do income verification.