So just posting an update:
In the end the only way I could get the shipment was by filling Form 39 myself. Had to pay 260 rupees as bribe to get it done and a 100 rupee affidavit was attached with the documents. Getting it done was quite easy since I had a contact who is a central government employee himself. Otherwise the sales tax guy was telling me he would've taken more bribe from me, so like maybe 500-1000 more perhaps. Anyways...
List of required documents were:
-To get Form 39 from UP sales tax department you have to fill a 3 page application. Form was in pure Hindi and at that moment I realized how much I sucked at Hindi.
-Attach a copy of the Invoice of the purchased product that you want to ship in UP.
-Attach the credit card statement showing proof of purchase or any other document for the relevant mode of money transfer used to buy it.
-Attach the proof of shipper's address, where the product was stuck (not original shipper). So basically DHL's tracking detail showing the current location in New Delhi.
-Address Proof - here I used my Passport and Aadhar Card, one is enough though. You can use anything else like SBI passbook or whatever verified by government itself.
-Affidavit where I told them that it was for personal use and won't be sold for commercial purposes etc on a 10 rupee stamp paper. Plenty of people sit outside the building who will type it up for you. 100 was his fee.
-10 rupee stamp on actual Form 39.
So it took me like 1 hour and the Form 39 looks like this:
After that I just submitted it to the closet DHL centre which was close to my home and it reached its destination in Delhi by midnight. My RAM has been finally delivered, today.
Newegg's customer service is crap. Their chat system is very good but their shipping team is completely out of sync and slow. I kept waiting for their approval to collect it from Delhi but they took weeks to even reply it and I received their approval today but guess what? Yeah already have it now. So, be careful when choosing an address since Newegg can't change international addresses once they ship the item. Also their response time is very slow so don't expect any prompt help from them.
It's better to trust Amazon with this. Their international customer support is very efficient and fast and if it was Amazon then they would've given me the approval long ago and then DHL guys would've given me the package. Amazon knows Indian logistics and state rules better than Newegg which is still new with international shipping. Also Amazon's shipping rates are cheaper in comparison, at least in my state\city which is close\next to Delhi.
Anyways, I managed to get DDR4 16GB kit for just 14000 rather than paying 24-30K to Indian sellers for the same exact model. Very unreasonable prices here in India for DDR4 RAM.