Charlie - what kind of temps are you working in? (Don't make me jealous now).
I have an Edelbrock carb on my car, stripped the choke right off because it just does not need it, even in sub zero UK temps.
3 or 4 pumps of the throttle before I turn it over gets it every time. Even ticks over straight from cold startup - go figure.
What I do notice is that when I first switch on the ignition, the (electric) fuel pump takes a few seconds to refill the carb bowls - as you suspect, these carbs are prone to boiling/evaporating all the fuel out of the bowls as they stand. I can actually hear the fuel boiling in mine after hot shutdown. One of these days I will get around to fitting an insulating carb spacer.
If there is a problem with your mech fuel pump, track it down quick, as they can (emphasise can) leak fuel into the block/
oil sump.
HTH