There are reasons why this wouldn't have worked at all. I'll explain at the end, but first the numbers you ask for.
Liquid mass in Orbiter plumbing:
- Common feedline (between external tank disconnect valve and engine prevalve): 4000 lbm LO2, 250 lbm LH2
- Engine feedline (between engine prevalve and SSME): 298 lbm/line LO2, 22 lbm/line LH2
Using the engine flow rates from an earlier question of 925 lbm/s LO2 and 154 lbm/s LH2 at 104% and the same proportional assumptions, I get 3 engines running at 109% depleting the LH2 in 0.65 seconds and the LO2 in 1.68 seconds. (Bringing up more reasons why this wouldn't have worked)
Single engine running at 67% assuming it uses all the common manifold and one engine line gives LH2 depletion in 2.74 seconds and LO2 depletion in 7.21 seconds.
Why it wouldn't work:
- Closing the ET disconnect valves on a running engine(s) was considered catastrophic due to the water hammer that would result. Special pneumatic locks were added to hold the valves open after the Challenger failure.
- The propellant trapped in the feedlines would instantly lose pressure and the SSME turbopumps would cavitate.
- Propellant depletion shutdowns were considered catastrophic due to turbopump overspeeding, LO2 depletion shutdowns doubly so due to "burning and severe erosion of engine components"
References
- Challenger disaster: how full was the external tank at the time of destruction?
- https://science.ksc.nasa.gov/shuttle/technology/sts-newsref/et.html
- SMS mass properties page (personal notes)
