You asked about alternatives to the usual marketing avenues and there are more available to you as your flexibility increases. Here's what I mean:
Agents are restricted to the way they market a house on the MLS. We abide by Fair Housing and other industry rules that you as a private owner/seller aren't bound by. Even if you have an listing agreement with your agent you are still entitled to market your house with some of your own efforts. Remember though, that even if your efforts get the house sold, you will probably still owe your agent thier commission.
That said, you probably have a good idea (since you've lived there) who your target market is going to be. Just look at the demographics of all your neighbors. Once you figure out who you'd like to target your advertising to, go to where they are and put up flyers, cards, signs, blog posts, tweets, or whatever will get their attention. Most likely, you'll be able to highlight some buzz worthy things about your house that your agent might not be able to. When in doubt about what those things are, ask your agent.
As for being even more flexible, a few agents who've replied to your question pointed out the all-important PRICE. What hasn't been mentioned though is another big thing that attracts buyers: TERMS. There's a saying in the investment world that goes "I'll pay your price if you accept my terms." As people will point out to you, it's a "buyer's" market right now. But don't forget that another market dictates what buyers can and can't do and it's called the financial market. Many would-be buyers out there are having a hard time getting financing due to increased lending scutiny -- higher down payment requirements, credit score criteria, income verification, etc. Ask a few mortgage brokers if they've had to turn away more people recently and they'll probably confirm this for you. Advertising more attractive terms is a way to make your house stand out and appeal to those buyers because they are in a market pool that not many sellers are currently catering to.
But again, offering attractive terms will depend on how flexible you are in your current situation. It'll also depend on the quality of the guidance/options you receive from your agent or others you can find who know what they're doing.
In the past it was true that price (normal, acceptable to private homeowner pricing that is) would overcome other factors like condition/upgrades/cosmetics, but these days in so many areas there is an oversupply of homes on the market. Buyers have a lot of choices these days. If you're home isn't showing well it'll easy get passed because there are plenty of other properties for buyers to choose from. I don't practice in Memphis, but I do know someone who is in the process of selling off all his property in Memphis (he just relocated to Nashville) and everything he's sold so far in the last year have been short sales (ouch).
However, based on the number of showings, price probably needs to be addressed first. Your home may be perfectly show ready, but no one knows because they haven't even given it a chance because your home may not be coming up in the searches of buyers and Realtors who are looking for comparable properties.
Also, if you don't get a contract in the next week or so I would consider taking your home off the market for a while. The price point you've given probably means a first time home buyer would purchase your property, and many first time home buyers have accelerated their purchase to close by November 30. It may be quiet for several months after that deadline since the buyers who would have been buying during that time already did. The good news is that a lot of people think a new tax credit will be passed - at $15,000 which many analysts say will drive up home prices. If that does happen, you may be able to sell your home for more next year when it'll be fresh to the market again.
If you need help finding a realtor in Memphis, my friend knows some great ones. Just let me know.
The plain sad simple truth is that in a market like this, it always comes down to price. The ugliest house on the block will sell for the right price.
The fact that you have had only 3 showings in 3 1/2 months means that people don't even want to bother coming in the door. Even if your pictures are terrible (and I think pictures rank #2 in importance behind price) your house would get interest if it was priced right.
I do not know the Memphis market at all and I don't know your home, but price is the safest generalization an agent can make regarding why a house isn't moving.
I am sure (or I should say, hope) your agent has shown you sold and active comparables. How does your house place among the competition? A good idea for sellers to do is go around with their agents to active comparables and see for themselves what their competition is. Because don't forget, that is what this is, a competition.
Marketing is important of course but the internet presence you mentioned above pretty much covers what you need. Buyers have tremendous access to information about inventory. They are usually very aware of what your competition is.
As an agent, listing houses these days is, for the most part, emotionally wrenching. Selling is difficult under the best of circumstances and these are not the best of circumstances. It is very difficult to have to tell people that the biggest asset they own has "turned" on them.
I hope I have been of some help and I wish you all the luck.