I found original Election Commission of India shapefiles containing constituency boundaries prior to delimitation using the Wayback Machine. These shapefiles are available here:
Note that when you project the Parliamentary constituencies (anything from the "PC Boundaries" file in the link) using EPSG 4326, the constituencies are projected correctly.
However, when you attempt to project Assembly constituencies (the "AC Boundaries" file in the link) then, using EPSG 4326, the constituencies are projected to the west and are much smaller than they should be.
I have tried using every possible projection that comes to mind when dealing with Indian data, however, I am at a loss with regards to several points:
Does anyone know what kind of transformations could have been applied to this data causing the highlighted issues, and, even more importantly, does anyone know if it is possible to reverse these?