I'm aware of the risk of the bank calling the loan.

Even though the private loan won't be on my credit report, a loan is a loan and my traditional lender would be aware of me making payments to my private lender.

The scenario @Marko Zlatic described (unfortunately : ) ) does not apply to me but I still feel that it gives the feeling for people that the property is managed professionally and people are not aware that I own the place, which I would prefer...

Most banks will do this, but there are limitations to be aware of

Unfortunately, I never claimed depreciation the entire time I owned it (except for tax year 2021 when I finally was made aware). 

While any property can get bed bugs, if you are buying property that is very cheap and has cheap rent, especially for the area, I would be aware of the tenant pool you are pulling from, and make sure that you are okay in your head with managing a property with that tenant pool. 

I'm aware that things that sound too good to be true often are, which is why I'm trying to investigate a bit more about the potential downsides, but have had no luck with lenders.

I’m fully aware that this would be complicated and I’m hoping to gain insight and knowledge from pro’s who do have experience in something like this. 

By establishing clear policies and procedures, and making sure your tenants are aware of their rights and responsibilities, you can set clear expectations and prevent misunderstandings.

You are aware of 1031 Exchanges for that second property you are going to sell right??