I will bite...
I didn't see "last resort: Put it in a taxable account index fund." Actually that would probably be my first resort, read on...
First off, I ran a very quick amortization scenario on your old and new mortgages. I had to make some assumptions, but you can probably clear them up pretty fast. Mainly, I am assuming the 195k you quoted was the financed amount, not the total purchase price, since you didn't say how much you had put down.
Old mortgage P+I: 1032/mo. New mortgage: 1059. I assume taxes/insurance are the same (why wouldn't they be) and that neither loan has PMI. From a monthly cash flow perspective, you are about the same, as the $27 increase is in the noise.
In the meantime, now you have 77k in cash. Less the closing costs obviously. If my assumptions above were right, you had paid about 74k of P+I over 6 years, of which 24k was principal. So from a cash in to cash out perspective, again it looks like you did ok, as if you had lived there the last 6 years for "free". Again ignoring taxes and interest.... it's like you got all the P+I back out.
I would now look at it through the lens of: what is the power of the 77k. Using the 4% rule, 77k is worth about $3080/yr. Without going into specifics about which investment vehicle to use (which I know is the main point of your question) using the 4% SWR you'll now have recouped the closing costs within the first (upcoming) year, and have a nice chunk of cash to do what you want with. Which now is getting to your question.
If I was in your shoes (and my pencil-thin-stache investment accounts are currently funded to a similar order of magnitude as yours) then I'd invest the cash in index funds, in taxable accounts as necessary, while continuing to max out the rest of the stuff. I too am interested in eventually getting into rental real estate, but don't want to start on that until I have a nice solid stache of "lazy" investments compounding and working for me. For me, that means a nice fat figure in index funds... it could mean something else for you. But 77k even in a taxable account will nicely kick start wealth accumulation. Again, at 4% that's 3k a year (on average), which is not bad. A really good rental property would gross more than that, but I am not the expert on running rental numbers.
Others may chime in regarding your other ideas. 5k for a side business sounds high to me unless you have a killer business plan. Which you might, who knows. Again, I would park that 77k in an index fund in a taxable account and watch what it does for a year or two. It may give you some different ideas besides what you've listed above.