Sorry been away till now.
And I found some better diagrams, at least for me they are better. Edited yesterdays diagrams posted above.
Basically, you are just changing from what was working for 240 volts over to be 120 volts now.
Here's my take on what you have, I've added ID's in pic to all wires.
IMPORTANT: T2 and T3 will needed sorted out as to which one is which, because we will be splitting them apart for the 120v hookup, that sorting can be done w/ a continuity or ohms meter.
Numbers T1 and T2 are low or shorted to one another and likewise T3 and T4 are to be low or shorted to one another. Mark them accordingly as all the others I ID'd in the pic.
Changes to wiring inside that drum switch look to be not many major moves...you may have just enough wire length.
But, if it comes to working with those short wires you can just pull them six short wires back out of the switch and route them into a splice/junction box. Then from the added JB you may splice longer length pieces of wire to do whatever comes in the drum switch. Remember...current at 120v will now be double
what it was at before at 240V, so no "skimping" on wire sizes.