Firstly, Do Si Do hints at a couple of things:
1. It's a dance move that involves circling around
2. It's a move that's generally seen in square dances
So if we take words from the note based on:
Indexed positions that are square numbers, we extract:
Take steps these all repeat It's then then prime and and Just words left A numbers these the all step A to remove to reverse the jump right
Or:
Take all prime numbers, reverse
Then following that instruction:
So, indexing prime numbers:
Take steps these all repeat It's then then prime and and Just words left A numbers these the all step A to remove to reverse the jump right
Or (when reversed as per initial instruction):
Remove all these words and then repeat these steps
As per this new instruction we:
Remove all the used words to give:
It's then and Just left A the step A to to the jump right
Then repeat the initial instructions to give:
It's just a (from squares) jump to the left, and then (from reversed primes)
Leaving us with:
a step to the right (though it arguably should've been "A right the step to" to continue following the pattern...)
Now that text is obviously a reference to:
Time Warp from The Rocky Horror Show, which is also hinted at by other clues sprinkled throughout the text (thanks @tmpearce), such as:
- The Professor's name is O'Brien and The Rocky Horror Show was written by Richard O'Brien
- The "half-eaten dinner" is covered in "Indian spices" and the lead actor in Rocky Horror (both stage and film) is Tim Curry
- The "half-eaten dinner" is a "slab of ground meat", which may hint at Meat Loaf's role in The Rocky Horror [Picture] Show
- The inspector's name is Bostwick, which mirror's actor Barry Botswick who stared in TRHPS
- The colleague Dr. Adams may hint at Jonathan Adams another star of TRH[P]S
So I'm assuming that "the elaborate contraption [Professor O'Brien] has been working on for months" is:
A time machine. And more specifically, our Professor is in fact the Richard O'Brien" and he's gone back in time to the early 1970's in order to write and produce The Rocky Horror Show (the Story from the title), which will run at the Chelsea Classic Cinema on Kings Road (the Road from the title) from '73 to '79.