Pay off the mortgage.
But at the same time, sign up for a HELOC which you expect never to use but could use as an emergency fund until your cash emergency fund re-builds, which should happen very quickly once the monthly mortgage payment is gone. The thing is, if you define your ideal emergency fund as a certain multiple of monthly expenses (e.g. 3x or 6x), the size of the fund goes down a whole lot when you don't have to factor in a monthly mortgage payment, giving you a double-effect: cash builds up faster without the mortgage payment going out the door, and the target size for the emergency fund is smaller.
Don't forget to set reminders to pay real estate taxes and insurance yourself -- typically, the mortgage company pays those automatically from your escrow account, but you lose that convenience when your mortgage is gone. Those bills only come once or twice a year in most towns, so you need to forecast and budget up for them.
Most people here will tell you that your "investment is off the table" attitude is wrong and counterproductive. And as a general matter they'd be right, especially if you want to quit your day job before age 65 and live off your savings and investments. And, to a lesser extent, if you want to seriously augment your social security income. But you know, the only thing that's worse for your financial freedom than not investing in a balanced long-term stock and bond portfolio, is investing in that portfolio and then reliably selling low in a panic whenever the market swoons. So read up on investing, do your best to overcome that attitude, but if you honestly cannot, then you have to start thinking laterally.
So what do you mean when you say "investment is off the table?" It seems like you mean "no stocks, bonds, mutual funds and such-like," given that you are demonstrably happy owning real estate (the house you are about to pay off) and keeping your money in the bank (as opposed to gold coins under the mattress). The scary story you tell is about the collapse of Lehman, a securities brokerage, and not about being underwater on a mortgage or seeing your house value tank during the 2009 recession or watching your savings vanish in a bank failure. So what else might you be comfortable owning; something that would appreciate in value and/or throw off some passive income? A long-dated CD that at least has a higher interest rate? The house across the street, which you could rent out? Farmland in the rural part of your state which your agent could lease to area farmers? A bar of gold?
By the sound of things, you'll likely accumulate another big pile of idle cash within the next six months or a year, given that your income/expense situation has allowed you to build up your existing mortgage payoff fund so fast. It's important to find a way to store that wealth in a form that will allow it to grow and work for you. Plenty of people have retired early on real estate income, without owning a single stock or bond. In my view, that's not the ideal strategy -- but in your case it may be the best one that you are comfortable implementing. Real estate is one of the better alternative asset classes, so you would do well looking into it.
One or two final words about investment accounts and financial products: If your employer has a 401(k) plan with any sort of company match, I'd strongly suggest contributing enough to claim the full match. Every 401(k) will have some kind of cash-type investment option, if you remain committed to avoiding stocks / bonds / mutual funds, and the combination of employer match and tax deduction is a huge free boost. On top of that, I'd moderately strongly suggest opening a deductible IRA at Vanguard or an online brokerage like E-Trade and contributing the max ($5,500) to that every year. You will find plenty of cash and bank deposit type vehicles to invest in, the tax break will be valuable, and you'll have an excellent platform for stock / bond / mutual fund investing if you ever change your mind and decide on putting money in "Wall Street" investments.
Finally, at some point in your financial career you may come across a life insurance salesman, or an insurance salesman masquerading as a financial advisor who will try to sell you a large and expensive insurance product. For most people, who are comfortable investing in their own stock and bond portfolios, life insurance products containing value-accumulation features (such as whole life policies and variable annuities) are a pretty bad deal and should generally be avoided, because the management overheads and sales commissions take a big bite out of the underlying growth. Because at bottom, those insurance companies simply take your premium money and invest it in bonds and (in the case of variable or index products) stocks, and the money you get back in the end relies on those investments, just minus a whole bunch of needless costs and fees. If your goal is to avoid investing in stocks and bonds, this isn't a particularly good way to do it, and I'd suggest you avoid these products as well.
However, to the extent you have a spouse or children who depend on your income, term life insurance (which contains very little value accumulation and is for the most part a "pure" risk-mitigation product) is appropriate; moreover, when you are closer to retirement age, buying simple, low-expense, single-premium immediate annuities (up to the state guarantee limit for any given insurance company), which pay out a set monthly payment for the rest of your life, can help protect your money against your senility and/or longevity. If you are happy to put your spare cash into buying rental houses from age 40 to age 60 that's all good and well, but let's say you turn 61 and don't want to have to deal with tenants, or even deal with your broker / property manager who deals with the tenants? Sell the houses, buy annuities, live off the monthly checks, and give yourself a raise at age 70 by putting in for social security then. The insurance company will be investing in bonds behind the scenes, but with state guarantees in most places worth $300,000 per customer in each insurance company, you aren't exactly relying on the bond market as such.
