Sounds like a well handled situation.
I think what B737SFP is referring to is the FCOM1 Supplementary Procedure for deicing which should be on or around page SP 16.8/9.
My operator has no restrictions on an engine bleeds takeoff after anti-icing that I know of and publishes no specific guidance; the only warning I'm aware of is that in the SP section that smoke may occur during takeoff. The amount of times such a procedure is required (i.e. bleeds off takeoff after deicing) is probably why we haven't had any specific guidance whereas a Canadian operator is sure to have much more exposure and experience.
I think your hypothesis about the fluid shedding from the wing at higher speeds is credible. I suppose another possibility is fluid that was used to treat the runway surface being ingested due to the amount of spray being thrown up by the wheels and engines during the takeoff roll.