I understand that the Nayaka dynasty (succeesors of Chola dynasty)(1532-1673 A.D.) founded by Sevappa Nayaka started this as Royal palace Library. King Sevappa along with a Learned Brahmin, Govinda Dikshita(r), embarked on this ambotious program. Govina Dikshitar was associated with Nayaks court from 1575 to 1634 and was patronised by successve Nayak Kings.
As you said, it is only during Serfogi's period this library reached its prominance.
I am writinf an article in 'Wikipedia' on this subject & expected to complete by this month end.
Your Listing is a "very useful contribution", and thanks for your concern in connection with others who will be interested in same.
I made my first visit to Saraswathi Mahal Library in 1980, and spotted a very usefull "publication" of an Olai Suvadi from this Library Collection - namely the Kulothungan Pillaith Thamil which speaks of Rajendra Chola - 1, Kulothunga Chola - 1 capture of South-East Asian countries. Please see my research article on same uploaded to PSVP Files section under the caption "Virarajendra pdf"
Now that you have spent more time and investigated much on the Library's contents than my brief visit to same, I very kindly request you to let me know if you are aware whether their is a printed Catalogue avaible in this Library "on the entire collection of the Tamil Ola Leaf Manuscripts that are available in this library - STILL TO BE PRINTED & PUBLISHED".
This will be of much help if available, and possibly we could identify some very valuable Tamil Ola Manuscripts on History and important Literary and Fine Arts Works which we could highlight and make a request to the Authorities of the Saraswathi Mahal Library to give priority and publiah them, so that we could un-earth more historical informations on Tamil Nadu history, Culture & Literary traditions, as we have found in the Kulothungan Pillai Thamil already published by them.
Understand that there are 52 catalogues on tamil manuscripts that are being computerised.
I will get additional information on this (I am expecting input from my contacts there)
Meanwhile, reproduced below a brief writeup on Tamil Manuscript section of the Sarasvathi Mahal lib.:
The Tamil Manuscript Section comprises of 3780 manuscripts of which 2083 are Literary and the rest are Medical. All these are in palm leaf and are of the following categories: -
Rare Works like Kambaramayana, Kalingathu Bharani, Moovarula etc., are available in palm leaf manuscripts Unpublished portions of classics. Saiva, Vaishnava and Jain works. Later poetry of all descriptions. So far, 20 volumes of Descriptive Catalogues are published. Some of the rare works belonging to the Imperial Chola period are written in manipravala style. The medical manuscripts written by the Tamil scholars like Kottaiyur Sivakolundu Desikar were based on the process made in the Dhanvantri Mahal Hospital. Sivarahasyam, which was written during Serfoji I, is one of the oldest Tamil manuscripts, Kumbakona-p-puranam, Sarabhendra Bhoopala Kuravanchi are the notable manuscripts. The18th century "Kambaramayanam" palm leaf manuscript with 537 leaves and seven khandas is also a typical one. In 'Thiruvaimozhi vacaka malai' the line drawing of Lord Renganatha with his consorts can be seen.