Usually the bank will accept a fax, but it does depend upon the bank, certainly.
Yes, xe.com uses electronic clearing in both the US and Canada. They do have a default upper limit ($10,000) as I recall, for outstanding transactions (so one transaction, or multiple smaller transactions) but you can ask them to increase that limit as well. They've worked really well for me, with substantially better rates than I could get from a Bank. Indeed, several years back we were moving $10,000 from a US Bank of America account, and the difference in rate was about $500, although Bank of America was faster because it was a wire transfer.