I also require proof of savings of at least 2 months living expenses. 

Some neighbors also told me that there seems to be more people living in the house (on the lease its supposed to be the lady and her two kids 4 YO and 8 or 9 YO).

This will get you 90% of the way there and should be sufficient.It works the same in a saturated area, it's just more to sort through.You are aware that STRs in Denver are allowed only in certain zones and you must live onsite?

I own one half, 3 bed 3 bath, and I’m currently living in and renovating it with plans to rent down the line.

Almost anyone with a real service animal, would have had it with them at the viewing.On the application next time, have a box that asks if they have an animal that will be living with them-not a pet, but an animal. 

The couple living there was elderly when I was growing up, and we recently found out that they passed away a couple years ago.

On the flip side, if you've got a bunch of Section 8 tenants living in a building that's in a neighborhood where a lot of the tenant base has good jobs, high credit scores, and are generally reliable people, you've got the most risky tenants in that tenant base and that ain't what ya want.

It's near where I live though.

I lived there from 2017 to 2022 and personally witnessed significant changes during that time.

The only exception is for on-site managers, like you'd find living in one unit of an apartment building and managing the building on behalf of the owner.