This is a waffle with pictures, exploring modes of RC/"drone" (and I do use that term in this context lightly, with contempt heh) and making/displaying models.
Some of you may be familiar with novelty desk toys, such as a British Timelord's desktop ride toy,
or maglev toys etc...
some may also have seen RC and model rockets/jets with a Trek theme...
others may have also seen German, Japanese and American blimps for parades/ambiance...
I think though, what AST people were wanting,
was a type of Mylar Lifter, and a lightweight model upto 1KG, that can affordably hold up the model or display the model in motion, for a while...
and as we've discussed elsewhere here, it might be feasible.
checkout the RI and MIT vids, Googler and TedX vids (on new batteries, memory plastics, propulsion systems, PCB replacements, etc),
and GilbondFac on youtube - that guy is a genius!
The actual model might have more, or fewer Mylar Lifters, fans/propulsion systems, or battery zones... the makeup of the model may also necessitate different placement.
Also not shown are 'magnetic bumpers' which would prevent collisions from close-formation flying via repulsion with the other craft... (potentially a tactic for dogfighting).
So, the idea is that the model will have some design considerations;
we can apply the Kipling Method, and SCAMPER at initial concept brainstorm -
ERoEI, heat, EMR and other considerations are factors identified.
we will need lithium lightweight battery, or preferably graphene newtype battery (weight, 8.9grams, charge time: 8hours)
the internals and outer model shell cannot weigh more than 500-800 grams at this time, system total mass, for the object to satisfy the safety and lift endurance criteria.
Steering would be mapped to a bluetooth/wireless controller (of PS or XBOX style variety), or an RC controller - and would function similarly to RC planes or 'tanks'
pushing left on the joystick would slow the right side fans, increase rightside mylar lifter lift rate and lower left liftrate...
pushing up would increase the fan speed, and would increase the bridge mylar lifter more than the tail lifters (but all would increase).
pushing down would kill the mylar lifters and slow the fans... etc.
Of course, later, the movement patterns could be refined to reflect the motion capabilities we saw on screen. The idea is that, the vehicle will be able to fly for say, 1-3 hours, before needing a rapid-recharge from an induction pad that the ship can land on. It could even be programmed to be a 'floating display'.
The project concept is to have as much verisimilitude/good design finish to the on-screen vehicle as possible, while also being able to 'fly' the model for a long time, preferably in display with other space models - without wires or display stands.
This means no external propellors, or blimp lift bags, or wires.
Noise and health concerns are also a consideration.
Well, thats my rough ideas perspective and feedback for your concept -
bear in mind, I am a lay person, and haven't tested this, but for back-of-the-envelope,
I think this is plausible, would meet much of your criteria and budget envisaged,
and I am certain that Infomechatronics/puppeteers or local RC model clubs or 3D rapid manufacture clubs at your local uni. would be able to help you explore this even further.