HI Brandi!
I think what you may be running into is just a bit of confusion about the lending side of the house. Easy fix. First, your primary home was probably what is termed a conforming loan. So there are parameters that must be met such as credit, income evaluations, asset verification etc. They must do this because the loan will most likely be sold as soon as the loan is closed and you have made the first mortgage payment. This process allows for the capital to then become securitized and basically recycled to be used in future loans. This is conventional loans, usually owner occupied loans but there are investment property conforming loans.
You can transfer a property to your LLC with conventional financing, as long as you qualify for one of the exemptions. The one that sounds like it will most likely fit in your scenario is that you are a majority owner of that LLC. The borrower on the conforming debt must be a majority owner of that LLC, and in theory this will not trigger the due on sale clause.
https://servicing-guide.fannie...
Here is a link for Fannie Mae guidelines. Freddie Mac might be a bit different, so it is worth asking your lender about this if you are wanting to go down the conforming loan route (where you are being underwritten as the borrower for income, assets, etc).
Now there is another "class" of loans termed non-QM or nonconforming. That's a big wide field of options, but generally they do not check all the boxes for conventional underwriting on some level. Maybe they don't check credit scores, or they lend to businesses (LLC). Whatever it is, this non-QM stuff won't end up down the conforming pipeline. There are aggregators of loans that are non-conforming, with some stipulations of course for some level of conformity of the loans parameters. If you want to have an LLC be the borrower and you as a person are not getting the full conventional underwriting treatment, this is the space you are going to be operating in. A few options you might be familiar with are hard money loans (where they look at the asset more than the borrower), or a portfolio loan from a small regional bank in your chosen market that plans to keep that loan on their books and earn the interest from it. Obviously having an established banking relationship with them helps, so opening a bank account for your LLC with that bank you hope to work with in the future might be a good first step. As a beginner, many lenders are likely going to require a personal guarantee (often referred to as a PG). That means should the asset for whatever reason not fulfill the debt obligations if the loan goes into default, you are personally responsible for the shortfall in the difference. While these loans won't show up on your credit report, future lenders may ask about debt that doesn't appear on your credit report, and they will want to know what's outstanding that you are personally liable for, just for their own risk assessment.
I hope that helps clear up some things for you!