OK, this is going to seem contradictory - but speaking from experience, here goes.
Conjugal partner almost never works for US/Canada couples. The conjugal partner category waives the co-habitation requirement of the common-law qualification because of exceptional circumstances. Section 5.45 of the
OP2 Processing Manual says this: This category was created for exceptional circumstances – for foreign national partners of Canadian or permanent resident sponsors who would ordinarily apply as common-law partners but for the fact that they have not been able to live together continuously for one year, usually because of an immigration impediment. In most cases, the foreign partner is also
not able to marry their sponsor and qualify as a spouse. In all other respects, the couple is similar to a common-law couple or a married couple, i.e., they have been in a bona fide conjugal relationship for a period of at least one year. Because of Supreme Court decisions, the choice not to marry is a constitutionally protected choice. Thus, CIC cannot require couples to marry in order to immigrate. However,
if they are not married, they must be common-law partners. There is NO provision for fiancé(e)s or “intended common-law partners” in IRPA.
If a Canadian and a foreign national can get married or can live together and establish a common-law relationship, this is what they are expected to have done before they submit sponsorship and immigration applications.
So, on the one hand, you're right to pursue common-law qualification - if you can't get married. (If you can get married, make it easy on yourselves and do that.) The problem is that CIC is not going to be helping you accomplish c/l qualification by automatically extending your six months status to another six months just so that you can qualify to apply for permanent residence as a c/l partner. Part of how they do this is they avoid documenting US citizens when they enter Canada to "visit". Once you're admitted, you're allowed to stay for up to six months, and this is pretty much on the honor system . . . they will not give you proof of when you entered the country. This makes it hard to apply to extend. If you do get proof of your entry, and you apply to extend before your 6 months status expires, you've got to have a valid reason for staying - and staying so that you qualify to apply for PR as a common-law partner won't fly. If they wanted to allow foreign nationals to come into the country and simply live with a Canadian partner for a year in order to become common-law so they can qualify to apply for permanent status, they wouldn't limit stays to 6 months!
Your best option, really, is to leave Canada just before your six months is up and then
try to re-enter for another six months. Problem is, there are no guarantees that you'll be readmitted - again, especially if they get the idea that you're trying to live with your boyfriend so you can qualify to apply for PR. The second issue is that you really need to be careful in documenting your evidences of common-law qualification if you do manage to stay in Canada for a year . . . and you also need to be mindful of what you will do once the one year qualification period is up - because that's just the beginning of the wait. What's important to understand is that the common-law category was designed to allow Canadians to sponsor someone who is already their common-law partner. You're looking at another 6-12 months, potentially, before your PR application is finalized . . . still without being able to work. From someone who's been there: this can be very stressful on the relationship and the finances. I don't recommend that you apply inland AT ALL - apply outland. Some people make the mistake of thinking they have to apply inland because they have to in order to substantiate the co-habitation . . . but inland and outland processing isn't so much about where the applicant is living - it's really only about which processing office is going to assess the application. Your evidences are what prove your common-law qualification -
not which CIC office processes your application.
So think carefully about how to proceed and, as I mentioned earlier: if there's nothing prohibiting you from marrying, you'll do yourselves a favour considering it.