[gphilip]

Here is one thing you could try:

1. Identify research scientists (e.g: in Google/IBM/Microsoft/... research labs) and professors (in institutes/universities) that you would like to work with.

2. Write to them directly, attaching your publications and requesting an internship.

Depending on how your publications are perceived, there is a good chance that at least a few will choose to engage with you.

Indian institutes funded by taxpayer money are required to follow a prescribed set of rules for selecting PhD candidates, in the interest of ensuring fairness, preventing nepotism, etc. . The competitive exams that you seem to loathe are part of this process, and professors can do nothing about this.

They have much more leeway in choosing interns, though. The rest follows as per kubrickslair's recipe.