Taking out a HELOC to invest is something many here do, but there are only two things to consider if you're talking about converting your mortage to a HELOC.
What's the REAL cost of the mortgage vs the HELOC (including both now and in the future), and what does it do to your cashflow?
I'm concerned you even mentioned PMI. "No PMI on a HELOC" is like saying "our broccoli is gluten-free." Well, necessarily, yes. You can't get a HELOC without equity, and you have no equity if you're paying PMI.
If you could really convert a mortgage to a HELOC and save a fixed 1% on interest or something, it could make sense. More likely, however, something else happens. Your minimum payment may skyrocket, imperiling your finances if you can't deal with the cashflow change. HELOCs are rarely fixed rates. Refinancing to a great variable rate might be lovely until it goes up. The HELOC may also offer interest-only payments at first, which hides the fact that you're ballooning your debt, and smacks you with a very large payment later, which you may or may not be in a position to cover. If you get a HELOC with slightly lower interest than your mortgage but pay only interest for three years, you swindled yourself (unless we're talking <5% interest range, verified interest savings, and no suddenly huge minimum payment or prepayment penalties or hidden fees).