Hi well any 6309 movement will fit and easy to obtain, or a quartz 7546 whic are also fairly easy to obtain but why not just fit a date wheel to your 6105 movement ?
You say you have a screw down crown !! are you sure because the 6105 does not have a screw down crown just one that locks.
ps: Assuming you are talking about a 6105-811X
Tiger...the screw down detail is what I have done in the past by putting an aftermarket Trip-lock screwdown crown in the case and sealing it with a metallic epoxy commonly known as JB Weld...I had to drill out the original crown tube and fit in the aftermarket crown threaded section into the case and keep the crown centered perfectly...
The only problem was using the Swiss screw thread female stem of the screwdown crown with the Asian male stem of the 6119 movment...I wound up filing the stem to a point and making it screw into the female portion of the screwdown crown, then sealing it with Superglue...between the JB Weld seal and the screwdown crown detail, I have worn this watch in hot tubs , saunas and Caribbean dive sites for years with ZERO sealing issues...always wanted to wear a 6105 while diving with no worries about leaks!!!!
Rich