In reality the ET is released on a suborbital trajectory and carrying
it the rest of the way to orbit will cost propellant, which is
something that most of the remaining flights (ISS assembly flights
packed to capacity) cannot spare.

Yes, given the "packed to capacity" this is true.

The real problem with the concept of making a station from spent fuel
tanks, though, is how to supply the rest of the station, other than
the structure. Cooling/heating, solar panels (or other power source),
electrical distribution, etc, etc all need to be added. Inflating
something inside the tank is perhaps promising. But still, adding
labor for people to do on-orbit is problematic.

So even aside from the issues specific to the shuttle external tank,
I'm not sure this is a promising idea.