In that case, I’d shoot at rocks, one shot for Canada, one shot for the US, until a ricochet gets me. Whichever country the shot was for gets to add me to the enemy body count. 
Since you are already married, your fastest route to citizenship may be military service. Apparently, once you have a green card, you can enlist, and then you can apply for naturalization almost immediately. Easy peasy.
Just make sure not to get a dishonorable discharge.
The info is on the USCIS website under “naturalization through military service”.
If you really love America, you would do this for us.
You could also commit an act which is considered a crime in Canada but not in the US, then flee to the US as a refugee. Historically this has worked for citizens going the other way (as in the case of American citizens illegally avoiding the draft); not sure if there have been any cases where it’s working going from Canada to the US, or what crimes this option would work with.
(Note that I am not actually suggesting you break the law; I am merely presenting this as a hypothetical way you could establish residency in the US with a view to supporting a subsequent citizenship application.)
Thanks for the helpful replies everyone, it is much appreciated.
Regards
Gus
I suggest lèse majesté.
Wait, what? Which diseases?
That’s an offence in Canada?!
Sorry, I crossfired on things that make you ineligible for admission to the United States as a Legal Permanent Resident. To become an LPR you have to have a medical examination by a public health doctor. The current list of conditions that make you ineligible to get that status: Tuberculosis, Chancroid, Gonorrhea, Granuloma inguinale, Lymphogranuloma venerum, Syphilis, Leprosy or “any other communicable disease as determined by the U.S. Secretary of Health and Human Services.” It is possible to get a waiver in some cases.
Other conditions that may render you inadmissable to LPR status are violent mental health conditions and drug addiction. Also if you fail to prove you are vaccinated against a number of vaccine-preventable diseases. Finally, certain conditions which do not present any medical bar, may make them doubt your ability to self-support, which is another thing you have to prove to get LPR status.
Sorry for the confusion there.
If you’re going to have “lèse majesté” on the statute books, at least do it properly! 
What an odd offence to have.
Of course, the really, really, difficult part is actually getting the green card. Once you are a legal permanent resident, except under some unusual circumstances, citizenship is just a matter of time, correctly filling out the paperwork, and paying the appropriate fees.
what’s wrong with keeping your old cit and having a green card? you could go back to canada every election season to vote for your favorite politician there.
Not after five years, you couldn’t.
I acknowledge that the above site is a little axe-grindy, but I’m in the situation described therein and it rather annoys me.
From what I’ve heard, getting into the US on a working visa isn’t exactly the easiest process. If I recall correctly, you have to have a company sponsor you and in doing so they have to prove they exhausted all other means to higher an American for the same job. As far as I know, the ‘easiest’ way to permanent residency in the US is to marry an American citizen.
I’m actually involved in the process right now with my foreign born husband. From the point of the initial application to now, it’s been 15 months and has cost us close to $1000 in application fees. And that was just to GET him here so we could marry. We’ve been delayed in the next step, which is going to cost us another $1000 because, frankly we don’t have the money. The forms are complicated, convoluted and a huge headache. The US government certainly doesn’t make it easy to get here legally, that’s for sure.
If you want a good resource, I highly suggest visajourney.com. It’s been a valuable source of information for me and many others in the process of becoming a citizen/permanent resident.
Does the OP play hockey? We could use another Canadian / American on our beer league team in MN. 
We have two already, though they both came to the states by way of attending an American university and then marrying an American.
Anybody remember that Seinfeld episode where George wants to break up with his girlfriend Moira, but she doesn’t want to break up with him? And Jerry says breaking up with someone’s sort of like pressing the nuclear button? Two people both have to agree to do it, because no single person knows enough to do it alone.
I think dual nationality is a lot like that. It isn’t illegal or void unless both countries say so.
Britain doesn’t recognise your renunciation in the oath as legally binding, either. If you started out British and want to take up your British citizenship again in the future, it’s no problem.
No, it’s simpler than that. Once you’re a citizen of a country, either by birth or some other means, only that country can say if you’re still one of their citizens or not. It has nothing to do with any other country.
I’m not sure why the need for a US citizenship. There’s lots of Canadians who spend a considerable percentage of their time in the US and even own houses in the states and never become US citizens.
Consider for example, the common snowbird. This migratory avian annually flies to such southern locations as Florida and Arizona for the winter but is careful to spend at least 6 months in its summer habitat (which can be anywhere from Moose Jaw to Moncton) so as to remain qualified for Canadian health care.
OK the OP is not a retiree, but since they’re not tied down to a specific location for employment, it seems to me they could do the same thing. Is there something I’m missing here?
It seems to be more of a heads-we-win, tails-you-lose strategy on behalf of the UK (and US) Department of State Departments.
They won’t recognize you as a citizen of another country if they want to prosecute you for a crime domestically. They won’t recognize you as being not a citizen of another country if the other country wants to prosecute you for a crime there.
It makes total sense that the UK would take a once-an-Englishman, always-an-Englishman approach. They wouldn’t accept, historically, that their countrymen might try to renounce their citizenship and move to the continent and take up arms against the forces of The Crown.
My perfunctory reading on all these “dual citizenship” policies is that their designed to serve the state, not the citizen.