North of the tunnel isn't a pinchpoint, and won't be for a long time. Between Carleton and Gladstone is one of the fastest portions of the line (85km/h) which means trains are able to get in and out fast enough to avoid causing backups.
Everything South of Carleton can be double tracked easily without shutting the line down and that's where most of the pinchpoints are. Once South Leitrim to Carleton is fully double tracked, then Carleton to Gladstone becomes a problem, but that won't be for a very long time.
The trench North of the tunnel is actually pretty wide (as I've noted before). It's around 8-9m according to Google maps, and with a realignment of the existing tracks to be closer to the trench walls you wouldn't need to blast a huge amount to get the width required for two tracks.
As for the new Hospital land, according to geoOttawa, the land plot for the rail line extends well beyond the edge of the trench.
Of course that might change when the hospital is actually built, but since a station was considered for that location anyway, I have confidence that the city will protect the land necessary to provide enough space for a second track in the future, after all it's pretty cheap to do that.
On a side note, i guess I never really thought of it like this, but they managed to install new signals without shutting the line down, so that's something. I guess they'll be taking a week to bring them into service next month, but...
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