Is it safe to "bake" these in an oven?
Not really, no. You wouldn't be the first person to try this and you might get away with it as some have in the past, but if it doesn't work as hoped it could lead to the only option being a complete strip and re-finish.
There is a potential health risk involved in doing this in the oven you cook in, but to focus on the woodwork you can't reliably do this in an oven with a minimum temperature of 170°F (77°C).
Warm is good, but that's a bit hot for safety. And in addition you can't be sure how hot the oven will get because most ovens don't hold at the set temperature the way we think — "hold" in this case being a misnomer since ovens don't do that at all. Instead they cycle on and off to approximate the set temperature. Additionally the thermostats of ovens are infamous among cooks for being off (reportedly by as much as 50°F!) which with wood is all kinds of bad as the water in it will turn to steam and bubble through your finish. I've seen it happen and it ain't pretty!
Or, could I place an electric space heater in the same vicinity as the items?
Much better option.
What can I do to speed the drying of these items?
Increase air flow (to begin with to take away the evaporative portion of the varnish, after that oxygen is needed for the curing process to progress).
Increase temperature (both reactions proceed more quickly at higher temperatures).
Decrease humidity (water vapour can retard varnish drying and curing).
Obviously that last one shouldn't be an issue for you.
As for the first one, in reality normal rates of air exchange for typical domestic interiors are enough for reliable varnish drying so the main thing to focus on is increasing the temperature. There is such a massive difference in varnish drying with only a 10° change in temperature just giving it a little boost should make a world of difference.
(I will wrap them individually in bubble wrap or similar when packed for shipping).
If there is the least tackiness still remaining it would be advisable not to put the bubble wrap directly in contact with the varnish. Instead cover the pieces in a smooth plastic (black refuse bags can work well) and then wrap in bubble wrap.
For next time
I can highly recommend thinning your varnish with between 25 and 50% additional spirits, turning it into 'wiping varnish'. This can be wiped on as the name suggests, or applied by brush or roller if preferred. Regardless of the application tool you then wipe away some or most of the excess. This builds a shiny finish much more slowly, but each coat is very much thinner so dries far more quickly and reliably than when the varnish is used at full strength.