I have to agree that on British India I think you are on a loser. I understand the problem, but as an army the British Indian Army looks like this:
The British Indian Army = all troops based in India, with senior officers often educated in India (look up Quetta Staff College) but all British Army
...made up of:
The British Army in India = British Army units posted to India; fully British nationality, part of the British Army
...and...
The Indian Army = Indian units, until WW1 with all British officers, but by WW2 with a gradually increasing number of Indian officers.
These units were mixed together in service; almost all divisions had both British Army and Indian Army units, so treating India as a separate country is really problematic in at least this respect.
All units were mainly supplied from India - there had been arms factories and artillery production facilities in India since the eighteenth century (1780s, from memory). All kit, small arms and support weapons were Indian made, as were some armoured cars (the start of Tata Automotive company), 25 pdr and other artillery pieces and escort naval vessels. The main items not made in India were tanks (supplied for the two Armoured Divisions raised from USA and Australia), aircraft (spitfires and hurricanes, at least, were shipped in in "kit" form and assembled in Ceylon) and larget naval vessels (which could simply be sailed there!).
I suppose you might make India a puppet with no army and no ability to maintain its own military units (give them all as Expeditionary Force to UK??), but it seems a bit of a stretch, even then.