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Here's the overview; I drew a cyan and a green line to represent different routing variations; they are mostly mix-and-match (so the green route through the U of C could be combined with the cyan route through the FMC, for instance.) An orange line shows an additional or alternate potential connection between the FMC and Lion's Park station, which accomplishes goal 2 and goal 1 if the green route to Westbrook is built, but doesn't accomplish the other goals. (But it is shorter/cheaper.) The lines are elevated 30m from the ground, to give a potential sense of vertical scale.
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Through Westbrook/Spruce Cliff, there's only one route that makes sense to me; the straight shot north from the LRT station to the edge of the cliff along Spruce Dr. I use a park to provide a potential turning station (or even a Spruce Cliff community station).
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In Parkdale, I think the location that makes the most sense is the City owned transit park and ride lot at Parkdale and 34th St. My fantasy is to build a modest highrise here of some dozen or so stories, with a gondola station on the roof connected to the ground by elevator. The Bowness/Parkdale/Kensington corridor is a strong bus corridor, so this could be a key connection.
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At the Foothills itself, I show two possible station locations. The cyan line goes to the entrance of the McCaig tower, which is a major lobby and closer to the teaching portions on the north part of the campus (important since this will also connect to the U of C campus). The green line goes to the cafeteria area between the main tower and the Special Services building; not as good a location overall, but it supports a second line or alternate path connecting to the east (the orange line). One constraint here is the helipad; both gondola lines are on the other side of the hospital towers from the helipad to avoid conflicts.
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Through West Campus, I show two substantially different alternatives; the green line provides a connection to the Children's hospital and some of West Campus, while the cyan line is more of a straight shot along the linear park; it could have a station where it turns towards the U of C, but that's fairly close to the potential U of C station shown. It's also possible to build a hybrid; the green path to the Children's hospital, then the cyan line where they cross. I think of the Children's hospital as a much less important node - it's much smaller in terms of employees and patients, parents are less likely to take their sick kids by transit, it's not as tightly connected to the U of C programs. The best station location for serving the ACH and West Campus is on the north side of the hospital around the intersection of W Campus Way / W Campus Dr, but that is much closer to the helipad. I don't know if the helipad could reasonably be relocated further away, or if the distance is appropriate and a station could be built there which would be better than either alignment I present; I leave aviation expertise to others around here.
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On the U of C campus, I have two possible routes shown. The cyan route is shorter and connects at the north side of the Physical Education complex; a little at the edge of the campus, but it has a nice straight shot towards Brentwood station. The green line goes to a station at Craigie Hall, which is more centrally located, but it passes over Mac Hall (3 stories) and the link between the Engineering and ICT buildings (2 stories). Potentially a turning station could be built here and the actual stop on the roof of Mac Hall, why not?
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The orange line goes through St. Andrew's Heights and Hounsfield Heights/Briar Hill, along 13th/15th Aves going over Crowchild. There are the potential for community stops in St Andrew's Heights at the corner of the schoolyard and in Briar Hill around 21A St. The route then connects to North Hill Mall and the Lion's Park LRT station.
The overall length of the system is roughly 6 km from Brentwood to Westbrook. At 30 km/h, probably the fastest possible top speed for a gondola, that is around 12 minutes end to end. Current transit connections are over half an hour, either 31 minutes on the 72/73 or 34 or so connecting downtown on the LRT; the drive is 10 minutes or so without traffic, so it could be a potentially attractive route, assuming fairly high speeds and limited delay due to stations.