Seems to me you have a 10-year warranty on parts.
From their site:
»www.york.com/residential/why-buy···ies.aspxAll Air Handlers Warranties:
All York® products come with a written limited warranty on parts. This warranty states that a replacement part will be furnished for any part of the product that fails in normal use and service during the applicable warranty period specified in accordance with the warranty's terms. Your authorized York® Dealer can review with you the warranty periods for the products you select.
In addition to this, you have a failure rate that exceeds normal use and normal wear. Thus they should be covering labour, or someone should be generating a refund cheque for you.
Your new furnace certainly isn't giving you peace of mind, eh? Say it just like that to York when you call them. Don't be shy to escalate this up the chain.
Also, as seen at the bottom of the webpage, their site is geared for all North America (references Quebec). Guess Canada just has "approved dealers" and nothing more?
They should be sending someone out for you as a quality call or on warranty for no charge to fix what your paid professional could not.