IMO, it's a difficult situation time-wise.
1. Your agent should have requested for CAN+ processing because you have valid US visas. This could have resulted in expedited decisions.
2. Your agent must asap send a Case Specific Enquiry/IRCC web form + an email to the Bangalore consulate to request for expedited decisions. He must include copies of your US visa + your US-India and US-Montreal flight tickets + any evidence of meetings scheduled in Montreal.
3. Assuming you get passport requests in the next 2-3 days before you leave India, you won't be able to submit your passport for visa stamping to VFS Chennai. You won't get your passport back in time for your US travel.
4. Your next alternative would be to submit your passport to the VAC/CSC in either NY/LA. You would need to closely follow the instructions for submitting the passport/paying the VAC fees for passport submission in the US. There's no scope for making a mistake.
The US VAC/CSC advises to factor in at least 15 business days for passport transmission/visa stamping. This would mean you'll be on tenterhooks for your travel to Montreal.
IMO, you would want to postpone your Montreal meeting by 7-10 days + do ask your travel agent to go ahead with Point 2