Transfer holdings from NRE DEMAT A/c to another Indian Resident DEMAT A/c

I have an NRE DEMAT Account with HDFC Securities in which I hold a portfolio of stocks.
Now I have returned back to India and I wish to open an indian resident DEMAT Account with another DP (i.e. non-HDFC).

My question is:
1. can I transfer the NRE DEMAT holdings from HDFC securities to the newly opened Indian resident non-HDFC DEMAT Account directly ?
2. should I first convert the NRE DEMAT in HDFC to Indian resident DEMAT in HDFC itself and only then transfer the holdings to the non-HDFC DEMAT Account?

Also noting:
HDFC Securities is part of NSDL while the other DP is part of CSDL. Will the procedure be different in this case?