You said you are naturalized USC. So I would assume you have an idea what immigration really is.
You talk about getting visas like it’s a walk in the park.
I’m glad you have a lot of family and friends in India, but you are talking about immigration to the USA.
All new ballgame, all new set of rules. To get a visitor visa your girlfriend must apply, interview at the consulate, show strong ties to India, work, money…and most of all, she needs to provide proof she will come back to India…you have nothing to do with her tourist visa.
immigration - focus more on the required paperwork, marry, file, and hope your case goes smoothly.
to expedite a visa - another firm set of rules and requirements.
there’s no way around the legal process no matter how you ask and unfortunately separation from a significant other is inevitable.