I believe that chalukya Express initially started to cater to Bengaluru passengers however it's extension to Tirunelveli / Pondicherry was granted to provide a further connection from Bengaluru towards Tamilnadu. So I think that Rameshwaram extension will not be feasible with Chalukya Express.
A separate biweekly or tri weekly service can be explored between Mumbai to Rameshwaram via Hubbali Bengaluru Hosur Madurai and onwards to Rameshwaram.