You should be able to, yes. Are they actually rootbound? Height isn't necessarily a good indicator - if you can discern if they are rootbound, that would be more helpful, along with how many sets of true leaves? (not seedling leaves) I grew Castor Bean plants in the small peat pellets until they were 8 inches tall with several sets of leaves and branching, and definitely rootbound.

If your seedlings are leggy, then use a light source (I use fluorescent myself) and lower it to just a few inches above the plants. That will help keep them from being leggy and promote more substantial growth.

So really, there's no reason to not keep them in their current containment - just tweak things so that they get a really good rootstock so that when it comes time for transplant outdoors, there will be a bit less shock.

You could transplant them outdoors - keeping tabs on the weather forecast - and cover them with like 2 litre bottles that have had the bottom or top cut off so you can nestle the bottles down around individual plants like a mini-greenhouse. If there's a cold night in the forecast, get them covered in the afternoon to try and conserve some heat inside the container for the plant to last through the night. Then remove the covers/bottles the next day when the weather has warmed up for the day.

I don't usually start MGs indoors unless I'm going to be growing them in containers throughout the year, because they're such fast growers. Same with Zinnia. The Moonflower you refer to - not sure if you mean I. alba or any of a variety of unrelated plants that have that common name applied to them.