Remember the key to negotiations: what's your best alternative to a negotiated agreement? In this case it sounds like you don't need this deal at all -- you're highly profitable, right? Maybe there's some concern that if you walk away, this company could build their own whatever-it-is and beat you in the market, but it will take them some time and is not a sure thing for them.
The other thing to be aware of is the anchoring principle in psychology. By lowballing you at the outset, they make the range of offers that will seem reasonable to you.
I have not sold a company. But this sounds like a ridiculous deal to me. 3x revenues, in stock with a 4-year vesting schedule? For a profitable business??
There's a key number here you haven't provided: what's your revenue growth rate? If your revenues are growing slowly, then 3x revenues in cash might be a reasonable multiple. But if you've been growing at 40% annually, then 3x is way too low; 6x is more like it, and 8x may not be out of the question, depending on how large the ultimate market appears to be.
The big question for you is how you would feel if the deal fell apart. While you chew on that, you might want to see if you can find any other potential acquirers.
Involving bankers would change the tone of the discussion, eh? To what, I wonder? Really, this makes me angry -- it sounds like they're trying to take advantage of your inexperience.
It's your call, of course. But reading this makes me hope you tell them that their offer isn't even worth discussion, and walk away.