Few important points in my opinion:
-medicals deadline would be 30 days from the date of issue of form and approval, so dont wait for passport renewal
- most porbably, new delhi visa office might have asked for passport copy also.
- passport renewal in india, now with new current smooth process, will take approx. 1-2 months, if no other information in your current passport is changed. if you have any information change or if you have any country's visa pre-stamped(even travel), than it may take little longer time
- you cannot renew indian passport before 1 year of expiry.
- during renewal process, you will not hold any valid passport, old passport will be stamped invalid
- i dont remember which link, but for canada , for immigrants, they ask for atleast 6 months of valid passport when you enter the canada.
- like you and raman said, they need atleast 1 year of validity for issuing visa.
- understand, validity during issuing and validity during entering country is different matter, both needs to be taken care.
- there is also, 'tatkaal passport seva' available to indians , check
http://www.passportindia.gov.in/AppOnlineProject/online/faqTatkaalPassports
- so conclude, understanding your situation, i think, you contact new delhi visa office, talk with them.
- take medical, request visa office that you will update passport as soon as possible
- check what they say.
- important suggestion : always follow proper path.
- if any doubts, do ask without hesitation, we are not experts but have little experiance, which we are happy to share
- i may be slow in replies as do not check forum regularly. you can pm me if its urgent
GOOD LUCK !