I thought so there was a catch about a pull and push fan on the same setup, even though they would be on each other side of the rad/HE. That's probably we don't really see that kind of setup!
Isn't the hood blocking? I have 2 huge louvers in the hood to help air escape, would be counter-intuitive to me to block them off. Though I agree a lot of air does come out between the hood and windscreen.
The fact I don't use a shroud might also be a reason for hot idle.