You hire a plumber to fix a gas leak in your house. The guy's inept, botches the job, and your house blows up.

That is probably a tort and possibly breach of contract as well. The real question is whether or not Joe the Plumber has insurance or is independently wealthy.

If neither insured nor wealthy, the odds of anyone taking the case on a contingency are slim.

If it were taken as a breach of contract case, the problem would be whether or not loser pays was contracted for in the contract. If yes, then you could get fees and costs if successful. If no, then typically in a contract each side bears their own fees and costs regardless of who wins.

The other problem you have is the damages. Damages are typically nominal (sometimes called vindication) compensatory (actual out of pocket costs designed to make the plaintiff "whole") and punitive (conduct so egregious that it warrants punishment as well as making the plaintiff whole). Compensatory damages would be the value of the house, plus either lost rent (if a rental) or the cost of rent if it was were you lived, together with the loss of any personal items and, of course, any personal injury to the occupants (those damages would be specific to the injured person). Many jurisdictions have adopted rules (due to Tort Deform) to prevent double recovery, so if you had property insurance and it paid off, the damages might be reduced by that amount. What I have described is a general over view of damages - its not specific to your case.  

As for the specific facts you describe, I don't have enough info to determine if it is open and shut. I am not licensed in NY.

It sounds to me like your issues aren't so much with the tort system and whether we should use the British or American rules- in fact, I fail to see how the choice of fee system would help you here - but with the slowness of the wheels of justice.

Two different things. It sounds as though, notwithstanding costs to the other side, they have made a determination to fight it all the way. Look at the bills you describe. Do you think it has cost the other side substantially less?

The American system also relies on rational economics. The costs of maintaining or defending the suit should be a reason to find common ground quickly and settle, even if you don't get everything you want or think you deserve (that's why its called a compromise). The British system - loser pays fees and costs has competing incentives. The one I just described, and the one that listens to "this is open and shut" I can get it all back. This is also a good way to understand the limitations of  classical text book economics. It relies upon people being rational and making rational economic decisions and having complete knowledge to make those decisions. That rarely happens outside an economics classroom.

Again all of this is without specific knowledge of your case which may have other issues. I just want people to see and think about some of the issues I just described.

I also recommend you dust off a copy of Bleak House  and review what happens in  Jarndyce v. Jarndyce

Being "made whole" by a lawsuit is rare. All the law can offer an injured party is damages (money). That doesn't bring back loved ones, it doesn't bring back missing limbs. You must also take into account a defendant has a right to defend.

What tort deformers want is to avoid any consequences of wrongful acts. They want a system designed to make it harder to bring cases and harder to win. They want the British system because they think it will make people think twice before proceeding on even a meritorious case.  I don't see the fairness in that. I believe lawyers for their own protection need to educate their clients on what they realistically can expect and where they need to settle.