If you purchase a duplex, just be willing to do some sweat equity to improve the properties and make them even more valuable.

Would I be able to combine a loan on the tiny home and the loan on the land and get cash out as an improvement? 

You can also do this on your own, but the agent will be able to narrow down many options and if they're really good they'll uncover some gems or off market deals.What I suggest is doing basic deal analysis on each of the properties you visit and you'll improve the "math" skills that you mention you struggle with.

I rehabbed it with additional 15K in improvements.

In particular, with an investment into a property wherein a high degree of its value from "land improvements" you may be able to shelter 100% of your gains. 

My handyman says these rents are still under market value and I can increase by about $650 and one unit is vacant so room to improve immediately.

Find one that needs a little love and do the improvements and either long term rent and refi or get it set up for short term rental and refi. 

I could also - instead of investing in a new property - use some of the $ to improve one of my properties - I have a bunch of it that's awaiting renovation and could then be rented out.

I am a general contractor by trade and have thus far saved up money to buy all of my rental properties (and their necessary improvements) out of pocket.

The kitchens are all dated, the carpets are worn, and the landscaping needs some work.By making those improvements, we can increase the rents, which increases the income of the property and thus, the overall value.