is manual THS operation available in all flight modes or only when auto-trim is disabled?
It is available in all flight laws. If the A/P is on, using the manual trim will disengage it.
Incidentally, an elevator with sufficient authority to override pitch excursions at extreme stabilizer angles would need to be very large indeed
Agreed. But a look at the graph, after the first stall, you'd notice that up to around 120 kts, the elevator authority was enough to check both the stabilizer and the engine thrust moments, which is the reason why I wrote earlier that, had the stabiliser position been changed and/or the thrust reduced, it would have been a by-the-book stall recovery. (That's why it is quite important to
know why the THS didn't move : jammed or un-used ?)