Did U measured with multimeter that 12V is coming TO solenoid primary circuit when ignition is on, kill switch is RUN position and U push start button? U told that it works when put screwdriver over solenoid, so, if it then turns starter normally, no need to open starter. To turn engine starter have to had:
1. +12V from starter button to PRIMARY CIRCUIT of solenoid (U can measure it by multimeter esily)
2. +12V from battery to input terminal of solenoid SECONDARY CIRCUIT AND when 12V is coming to primary circuit, then also 12V have to be in output terminal of solenoid=> 12V goes to starter motor and turns engine. (easy to measure with multimeter)
3. IF U have still that very bad Lucas solenoid, its earthing must be also OK, as it groungs via its cover/case to ground. (easy to measure again with ohm scale with multimeter).
I throw away that Lucas long time ago and put Hitachi solenoid from newer Ducati modells(need small modification to primary circuit connections). No problems since with 750 solenoid. Hitachi neeeds own earth to primary circuit. 907IE have that Hitachi unit.
If starter motor is gone/blown/brushes worn out, then only way is to open left side cover of engine, as starter have 2 screws outside and one(!!!) from inside engine. Somebody have changed brushes without opening left side of engine, but it needs really small/young flexible fingers...
