@Tom TomásThere are two loan products that could potentially fit your needs.

Long worded I know and I apologise for being green as grass, I'm as new as they come to the game but feel I have a good opportunity here.  

He's the attorney who got involved to save Chief Green and who tried to get Louise Lucas out of office because she told police to "stand down" when rioters were destroying city property. 

Most product is 2 to 4 units residential duplexes to quad's or much larger properties.In AZ some people are putting up non-refundable earnest money of six to seven figures depending on the deals.You will have to put in the time and make tons of calls.

The core 4 is David Greene’s strategy for long-distance and made up of a realtor, contractor, property manager, and lender.

If there is currently a loan on the property, you should be able to rate term refi for a much higher LTV than the cash out limitation you cited.If you did it with cash, find a hard money lender that will give you a short term cash out type product and then once you have the lien recorded you can rate term refi it as above.Selling or leaving money in the deal is an option in either scenario.

Focus on your business, build success, and then use that success to purchase a property.David Green has a new book "Sold" in the BiggerPockets bookstore that shows what it takes to set up a successful business.

I ended up turning one of my units into an AirBnB during the pandemic because I couldn't rent it out even after dropping rent $200.I still think if you have a nice product in a nicer area like Wicker Park you should be able to get it rented....really timing is everything and sometimes you are luckier than others.

I am investing from Hawaii and found that David Greene's book - Long Distance Real Estate Investing' was super helpful.My advice: Contact a realtor and get on their mailing list, get pre approved, and analyze a property everyday. 

And as for trying to find a different lender, I thought they all pretty much offer the same product so there’s no real reason to shop around?