Folks just to let you know, you can easily get refund from your previous state RTO. I moved my vehicle from Bangalore to another state. Paid the required pro rata taxes in new state. Submitted all documents via registered post to Kormangala RTO (now HSR) and got back full refund.
All this without a single follow up.
TBH i never hoped that i will get the money but i just sent the documents and then never cared to follow up and boom about 5 months later got the pro rata registration charges in my bank account.
So you can do the same for the other state as well. Send via registered post so that you can file an RTI later.