Chances are that you'll need to pull a permit and will be subjected to the increased property taxes.

Especially if there is a reval or if permits were pulled (which I hope they were!)

I want to pull out 40k in order to invest in a new rental property.

Based on the extra $275/month - I'm looking at about a 12.5% ROI but even if we don't command that and pull off $750/month, we're still looking at over 10% and more importantly a better quality tenant situation. 

How much should we pull out if we refinance our 1st mortgage?

I'm struggling to find anything worth looking at twice but on a side note I'm currently only browsing and won't be pulling the trigger till around December.

If we were to refinance the rental to pull out the equity, could we:1. put the equity in a self directed IRA? 

I would make an appointment with the state or county health sanitarian and go over this before I pulled the trigger.. 

So no swinging hammers, pulling permits in your own name, etc. 

As I see it, your two best options are to refinance the property to pull out a significant portion of the equity and invest it elsewhere (but eventually pay capital gains when you sell the property), or to sell the property now and reinvest elsewhere.