I think it's worth a try. If the OP gets denied at the border with all supporting documents at hand (valid TRV/WP and/or VR, job offer, LMO and Contract), then he would still be able to send application to Vegreville. I did it once but it seems ages ago and a lot might have changed. I had valid multiple entry TRV as a worker, not from visa exempt country, new employer, new contract, new LMO, did a U-turn at the border and less than 30 minutes later had a new WP on my hand. A bit of a scary experience dealing with immigration but the officers were very nice.
Regarding applying for a new work permit at the border, this is what immigration says:
I have heard of one person who was not visa exempt and had a multiple entry visa who did go to the border and was granted a work permit but that was probably a mistake as the rules are clear. Still, it could be worth a try if the border is not too far away. If they don't grant it at the border, you can still mail it in and wait 66 days.