I think it is a good idea to write to the Jodhpur HQ in any case, out of courtesy.  If they answer, so much the better.  My experiences with branch offices (last time in about 2005) is that they really did want to see *something* official.  A letter from Jodhpur is best.  But also, be armed at least with a letter from your university or institution, as official-looking as possible.  University stamps are always good.  

IGNCA in Delhi has filmed many RORI manuscripts.  These RORI images are an exception to the general rule that the IGNCA will not give copies to scholars without a letter of permission from the host library.  For RORI, there is a RORI - IGNCA agreement that IGNCA may give scholars images of the RORI manuscripts they have filmed.  So you could start with IGNCA, since they generally answer communications.  Did they film the Euclid MSS? There used to be an online catalogue of MSS at IGNCA (or NAMAMI) but I think it has been withdrawn.

Best,

Dominik