Providence Place was the area of the Southern end of Chance Street and so from the description in Tewkesbury Alleys 1848 we would have Middle Road as the Northern end of Chance Street or an extension of it.
However, a question was often posed in pub conversation "What was (or is) the shortest road in Tewkesbury?" and the answer was given as a section of road between the northern end of Chance Street and Cotteswold Road which was crossed by the old branch line to the original Tewkesbury railway station.
The 1848 Alley List gives Middle Road as having a junction with Station Street, but the wording seems to suggests that it was somewhat longer than the local tradition quoted above. I think the local tradition wins here.
Every trustable source I have come across ties in with the above.
Just a note on New Street and New Road. These co-existed in 1844 (Pigot's directory) and both had a beerhouse. They correspond to Trinity Street and Station Street.
I will do a little more digging and see if I can come up with a more definitive answer to Middle Road.
Regards, Andy Hewett (Capper), tewkesburyhistory.com