@Jim C.,
Numbers, Numbers, Numbers.
The house you mentioned- you have roughly $21,000 into it- getting $850 rents? What is that, 40% return on your investment (cash on cash)??? (I honestly don't know, too lazy and not enough info to even roughly calculate). I'm thinking its much, much higher than 40% though...
But, if you sell- you buy into a higher priced market---- Can you repeat that 40% with your profit from the sale? I would think no. Even if you can- you are taking a chance... You currently have a golden goose (geese?)...
As you said- if you did cash out--- is there a more productive use for that cash? A very important question, including estimating what your new risks will be...
-Worst case (as others have mentioned)- why not Heloc or Cash-out-Refi (pick which is a better fit for your situation)--- and sit on that money/invest in something else(diversify for gains and safety)/hold it until your local market prices reset/use it to invest in a better market/better class of properties, etc.. etc... etc...
I know you just gave examples as did I--- but I think the takeaway is:
you have a good thing going currently---- make darn sure whatever you do ends up being better than what you have now (there's no point to voluntarily put yourself in a worse position...)
If rents are that good- Heloc and Cash out Refi seem to be the best use of your equity- if you run the numbers and are ok with your new numbers with the new Heloc or Refi... But, these methods are (of course) more risky than just doing nothing more- and only keeping the good rent checks coming in...
my 2.5 cents (adjusted for inflation)...
Jimmy