Avanti:
Hitherto, your career has been spent learning about good Pilot Judgment, and then teaching it. This most certainly is not good Pilot Judgment. As UAL T38 Phlyer outlined above, not only is this trip beyond your capabilities and experiences, but it is beyond your aircraft's abilities! In the end, what this results in, is shear madness.
A definition of "shear madness" is this: You - a pilot with no comparable experience, on any level besides basic flying, are considering taking a Cessna 172 SP - a four place, high drag (more surfaces to ice over: struts, gear, etc), 180 horsepower, six cylinder, single-engine, training, aircraft, into some of the most severe weather systems that can be found over the Atlantic Ocean, this time of year.
As an MEI, I would expect that you know the value of redundancy, and as a CFII, I expect you would have a healthy respect for your personal limits, and the limits of your aircraft.
One of the most valuable resources that we, as inexperienced pilots, have, is that experience and wisdom of those pilots much more experienced than ourselves. Avanti, you have several pages of experienced pilots urging you to not be so careless with your life.
I can tell you about my experiences with icing on both rated and not-rated aircrafts, extreme IFR (for that is what you will encounter), and overall sticky situations and poor weather; but it won't be any different that what will have already heard. Ice is probably the number one scariest situation I have ever encountered. I hope your client does not require the aircraft to have paint, because a trip this time of year, along that route, will quite probably result in ice stripping the paint off the leading edges; not to mention the overall damage to the leading edges, propeller, spinner, engine, cowling, fairings, and wheel pants.
As a CFII, I expect you would know about how fatiguing even just a two hour flight in rough Actual can be; and now you're talking about flights in such conditions, in excess of four hours, without an autopilot! My goodness woman, do you like cheating death, or is this your first attempt?
As if the weather over the North Atlantic (which, may I call to mind, closes down some naval shipping routes) is not enough, now you're talking about International Airspace - a whole other beast, with whom you don't have experience. Have you ever met an Icelandic National? Their accent is extremely hard to understand, until you develop an ear for it. Now consider that you'll be flying through: Portuguese, Aramaic, and Hindi speaking airspaces. To the naive pilot, this does not seem like an obstacle; with English being the language of Aviation. Well, I'm not sure about the Azores, but I know that French controllers have a perpetency to control in a variety of languages, not limited to: English, French, Dutch, German, Flemish, Spanish, and Italian; making listening on the radio very user-intensive and stressful. (For you frequenters of CDG, this isn't usually the case; I have only experienced it during flights in other than terminal areas.) Not to mention that the accents you will hear, will only be magnified by radio transmission, making communication all the more difficult.
Now its really piling up; but wait, there's more! Supposing you get through the Atlantic, now you'll be faced with some of the most volatile and dangerous airspaces in the world: Syria, Afghanistan, Iran, Pakistan, Iraq, etc. Considering our current Wars, most of these are best avoided; not to mention Military Flight Restriction Zones in Iraq and Afghanistan. Lastly, you have Indian airspace. Not too sure about lately, but Indian airspace used to be the dread of every pilot, because "Controllers" couldn't control worth crap.
In the end, what it boils down to is: what is the worth of your life? I know for a fact, that most training airplanes that have been shipped to that part of the world recentally, have been just that: shipped, via cargo container.