I am doing a 30 year conventional.  

The home had a conventional offer submitted the day we saw it and my realtor, convinced this was the best home on the market for the purposes of getting the FHA loan approved, proposed a strategy that involved an above-asking offer to ensure we had an accepted offer.

We were able to get a home that needed a good bit of repairs with a conventional loan, and they gained a ton of equity in it.

Conventional 30-year thru local bank

If you have no income you cannot close with a conventional lowest rate loan.

Would it be a good idea to still write an offer with Seller Financing in addition to a more conventional offer?

You can purchase a single family home with an ADU with 3.5% down payment using FHA loan or 5% down using a conventional loan or you can purchase a duplex with 3.5% down. 

I would refinance this loan to a conventional loan in your name (it will give you the best financing terms).

Then refinance the hard money mortgage with conventional permanent financing with a bank. 

Generally speaking there are 2 main types of loans for investors: “Conventional” and “Portfolio”Conventional - I'll define these as loans that come from Fannie Mae and Freddie Mac (if you recognize those names).