I would pay the mortgage and student loans as slowly as possible, but with only $4K in SL's I can understand the urge to just get rid of it so if you have to, go for it. fallstoclimb can tell you how good that feels. : )
Max the 401k's, max the IRA's (likely would have to be Roth based on income), and invest whatever you're comfortable with in a taxable account in stock index funds.
You don't mention expenses, but given the amount you've been able to save they must be fairly low, like < $50K maybe. I don't think you need anywhere near $55K in your emergency fund. You should keep some since you are conservative, but I would aim for maybe 6 months of mortgage payments plus 3 months of other expenses, then invest the rest. Even if the market declines temporarily you will have plenty of cushion. You clearly have a lot of earning and saving potential, so your investments should grow very quickly if you begin right away.
If you absolutely can't stomach investing, you should look into putting some of the cash into Bonds, T-Bills, TIPS, etc. I wouldn't do this with that much of my net worth, but I'm aggressive.
Welcome to the forum.