As a great grandchild of John and member of the family, just thought I'd offer some information based on my own research and reflections that might be helpful for yourself.
Ancient India was invaded and colonized by two primary waves of Caucasian ydna groups. The first - and more well known to Europe - is a branch carrying the R1a marker - which invaded the Indian subcontinent from the North - coming down from Central Asia. The pool population of this group was centered there and to the West along the southern tier of Europe until the last ice age broke about 12,000 years ago.
Those in Europe moved farther north into ice-free zones (Central Europe, British Isles, Ireland, etc). Some of their tribal cousins from the East (Central Asia) came into Europe later on in different waves.
The other Caucasian group to enter the Indian subcontinent was the L tribal group - coming via the sea - landing all along the Western coast of India - South to North - eliminating many of the native males - with many settling down with local females. The Hindu myths record many of these early battles and colonization events by the ancient 'Aryans' - though through religious lenses.
Both R1a and L were instrumental in the rise of Ancient India - as well as Ancient Elam, Sumeria, and Persia. Many of the Central Asian Turks who established the Ottoman EEmpire were, also, L.
Those who didn't settle down pushed farther North, meeting up with their cousins coming from the North (R1a) - and kept moving with the 'waves' of civilization, eventually ending up back in Europe; some coming via Asia minor over land and others through the Middle East to the Med, then through Ancient Greece and Rome - and then, today, on to North America.
Needless to say, it's not accurate to say that our paternal line is 'Indian' in the sense of what the population mixture of India is today or that we were 'from' India. We need to go back 10-15 thousand years to get a better idea of what the population and civilizational dynamics were when we showed up there - and how we got to where we are today.
Also, the Roma are not haplogroup L carriers. We aren't Gypsies! :)
Haplogroup L were a branch of what are known as Phoenicians. It's a rare haplogroup in Europe because not many of us ever made it there after landing in South/South West Asia and settling down in the civilizational centers that were built there in the ancient past.
Those of us who didn't get 'sucked in' kept going. And here we are - still going strong in the 'new' world.
Hope some of this helps! :)