Just to add a few more points to the last few posts:
I somewhat ,admittidely subjectively think that saying that "there are no people there [nose creek]" is almost a good enough analysis. I wouldn't be surprised that if a Cost Benefit were done, and especially depending on who were to do it, that the Nose Creek alignment would come out on top. Not necessarily because it provides a fully better c/b ratio, but the lack of faith I have in how they are done and what indicators would be being used. It might full well be that, especially at peak hours, the trains running on a Nose Creek alignment would do so at enough capacity to justify them running the route in the first place - and thus, aligning itself or better yet, going heads above the other existing lines as being a distinictively commuter line/service; built corresponding to a short-sighted, narrow-viewed manner, lacking full understanding of transit's (transportation's) system interaction with land-use and throwing the importance of accessibility and what by and large, a public transit system stands for out the window.
Cost-benefits are not the be all, end all and nor do they not contain a level of subjectivity, especially, and this may very well be offensive to some, if the people doing them don't fully understand what should and shouldn't be included in them, or that some indicators can almost impossibly be monetized.
So as for the alternative:
A quick look and probably rather crude Google Earth measurement gives a slope of maybe 7 to 7.5% going from the ground surface of Eau Claire to the top of Cresent Heights ground level in a slightly NE direction. Essentially what a surface alignment would then entail, yet and since I can't seem to find the U2s exact slope limitations, a pretty safe, average presumption is no more than a 5% slope under dry conditions can usually be operated on.
So forgetting that this option would also require a hefty sum of expensive property acquistion, as well as traverse over a gem of a park even before falling in line with center st itself, the physicalities are already a constraint.
Now assuming that this rather large obstacle has been overcome, the proposition under the pretense that property be aquired, is that the line run in largely its own ROW (ROW A) and underpasses at key intersections or with some cross traffic conflicts (ROW B). Obviously a ROW A would be the better choice operationally, and one needs only to look as far as 36th st to see why. However, both options would cause rather large seperation effects, with ROW B alignment slightly less so, and definitely adversely impacting the corridor as a desirable urban area and thus, its ability to attract. It may sound rather trivial, but the effect that a barrier has, potentially turning a 20 - 30 m walk into 1000 m is not. A desirable urban area, one with a corresponding focus on neighbourhood mobility can essentially not be acheived with a barrier that would have largely, the same equivalent effect as turning Center St. into something like Crowchild Tr N, would. Transit is good, but not if done wrong and with little regard for the sustainable mobility pattern needed in an urban area that would then feed it, i.e. walkers and bikers. If the goal is to also increase Center St. as a viable, people oriented, urban corridor, or a corridor of urban rejuvanation, then an at grade LRT whose concimitant goal is also to effectively serve outlying suburbs, is not a good option.
Thus, I also largely believe tunneling is likely the most optimal option. How far is another story, but any surface seperations that would stem from an at grade alignment would have to be handled with care, and not made to increase any seperation effects that Center St already poses.
As far as removing a lane or two of traffic. I'd say do it, but perhaps not with an alignment of the current style of LRT in mind.
Thus, and I do believe it has been thrown out before, maybe it is time to rethink the whole thing altogether: A big part of the C train's functional shortcomings is that it tries to do a lot of things at once. It tries to have relatively decent coverage, and it tries to serve outerlying areas with relatively quick travel times to the city core. It has arguably done the latter better. All this, while trying to be implemented very cheaply, and some of these characterstics have come back to bite it. Anyway, the suggestion here then being, that perhaps two lanes should be removed from Center and a Tram is run along Center, right over the current bridge and northwards. At slower operational speeds, it would then also be safe to allow these to operate along the whole street. Perhaps slightly raised just to give it more presence and also so that vehicles of course don't try to find extra lanes (so a ROW B), but if done right (that being key), causing no more additional seperation effects than center st already does if, not eliminating some due to two lanes of traffic less.
This, however, being only one part of the project. Where the other is then the start of a regional rail that indeed uses the nose creek ROW and potentially goes up through the Harvest Hills ROW (or stays closer along Deerfoot) for that matter and acts as an express commuter rail, which is largely what any kind of rail or even PT service that far out needs to act as anyway. It could continue on to that lovely place called Airdrie. (I'm not mentioning any additional land-use policy changes here along the corridor that would be required.) Provisions for a future station or two in Nose Creek itself could be required, if by chance, one day development would happen to occur in there more organicly. This line would also have to make use of its own infrastracture coming into the downtown, not using the current NELRT, and that starts to make costs of these two tandem projects look more in the neighbourhood of a tunnel
That is somewhat of a thought, and doens't take into account that such a Tram would then require another rethink of the SELRT, it's functions and objectives and how they would then connect. Another conflict. Or if they would then even connect...
The main point here being, as has been said, this needs long term thinking. Fifty to 100 year time horizons. Furthermore, the status quo and treating transit as an afterthought is another mentality that needs to go, and transit needs to be understood better as a whole.