Took a while to get the parts from Starbucks but my daughter's visit to London over the weekend paid dividends! The dome and straw came from COSTA coffee rather than Starbucks which may be the source of some of the problems I encountered with these pieces as described below.
The screw top insert piece was a very tight push fit into the main body although the thread worked well with the Starbucks drinks bottle. I ended up forcing it into its location and caused some damage to the layers in the main body in doing so.
The dome was a very loose fit onto the main printed part which is why I ended up using an elastic band to hold it on.
The straw holder did not fit properly onto the dome which meant that the super glue had to come out - unfortunately, there is not a lot of "touch" between the 3D printed component and the dome so I am not too confident that it will stay on for long. The hole for the straw was also a wee bit big - I cut down a pencil which had an eraser on one end to act as the perch.