I may want to purchase the SFR or multifamily I live in with a Conventional 97 or a FHA mortgage.

If not, you might just consider going 5% conventional financing and leave the equity in your current house and get a lot more cash flow monthly.

Rental comps and EMI numbers post conventional loan refinance, indicate $200-$300 cash flow. 

My suggestion is to you use a private lender or non-bank commercial lender, they will have more flexibility than traditional or conventional sources. 

I wonder if I can get a conventional loan under our new established LLC. 

Is it similar to a conventional loan where you have to put a down payment or can you do zero down if the seller agrees?

We also, recently purchased our first investment property (conventional 20% down) as well.

If you give them equity, you also give them risk and those that are investing in me would prefer to be segregated from that.If you're doing conventional cash out-refi's and are able to put their money to work for them twice per year (timing things perfectly) that's really a 12% annual return for them.

Thinking about this, with 10 conventional loans, you have the potential to buy $10 million properties.  

I closed on a house hack using a conventional loan in March 2020 with a rate of 3.625%.