I got the hyperdeck shuttle 2 to act as a convertor, and to also be able to record prores and raw simultaneously when needed.
Lag testing images here (i would assume the blackmagic convertor would be similar in lag):
You can see there's roughly a frame of lag on the BMCC screen itself, then one more frame going to the SmallHD DP6 which is either the shuttle or the DP6. I'm guessing the lag is from the DP6.
The Zacuto EVF has much more lag (3 or so more frames) but has better colour, especially red - even more so than the bmcc screen: