I believe that Raj is simply a corruption of Rajya. A lot of Hindi words were simplified when taken on in Anglo-Indian usage.

Then do you believe that Hindi rAj was borrowed back into Hindi from Indian English? I assumed that Hindi rAj < Skt rAjan 'king', and I guess that H rAjya < Skt rAjya 'royal, princely; kingdom'.

And Raj would be pronounced as a single syllable. The point is that, unlike Sanskrit, in Hindi in general use (at least the 22 years of use I had of it) the final consonant is not given the full value (with schwa) that it might usually be given in Sanskrit. Hence the Shiv/Shiva confusion, and simplification into either single syllable Shiv or made into Shiva with an 'ah' sound at the end.

This is what I noticed. In Sanskrit, you'd need to use a virama to suppress explicitly the default -a (schwa) vowel. But rAjya is pronounced with the final -a, isn't it?