[Mondial]

Yes, it seems more like a bad connection somewhere rather than a shorted winding. When you are drawing 10 amps of filament current, it takes only a tenth of an ohm of resistance to drop the voltage to 1.5VAC.

If the no load voltage remains at 2.6VAC and is constant then the winding is not shorted. If it drops with load then there is some series resistance somewhere in the connections causing the voltage drop. 

If the winding is not shorted but had an internal intermittent connection, then you possibly could use an external filament transformer to feed the filaments instead. That would be assuming that all the other transformer voltages were correct and stable.