Ah, I think I may have found my issue. Under Project Properties > Vision > General is a setting for Timezone Behavior that was set to 'UTC'. I switched it to Gateway Timezone. This was overlooked as we are not using Vision at all, so I didn't bother with those config settings, but if Designer inherits some properties of the Vision project/client configuration then that makes more sense all around.
After changing that setting and restarting designer behavior appears to match expected.
@pturmel, thanks for sticking with me, despite clearly assuming I was daft. That last little tidbit of knowledge was what I needed.
I'd still contend that it would make sense for the script console to run the same as the gateway context, but I'm sure there are reasons for it being the way it is. If I was doing more Vision scripting I'd probably want it left at Vision context.