Ya I want to increase the power density of EHD engines too, although to my knowledge nobody has done it yet, at least not publicly. Here's an example of a multi-stage engine by Jay Bowles at Plasma Channel:

https://www.youtube.com/watch?v=nrEBoPYS4ns

Unfortunately, I believe that his design is unlikely to be scalable, since each stage gets less than a linear increase in thrust due to losses. It's like stacking propeller blades. Each stage performs worse as more turbulence is added and the airflow gets less laminar.

IMHO the efficiency comes from the surface area of the anode (the wire). The cathode could be the lifting surface or body of the craft, so isn't that relevant for performance. Foils, pipes, anything works for the cathode. Taken to the limit, the anode might look like a 3D array of point charges, separated by thin insulated wires. Or a mesh with a high surface area to volume ratio. Something that looks more like a big ball of steel wool.

Some experiments have also separated the ionization from the electric field. Like in vacuum tubes, the hot plate can emit electrons regardless of the voltage between anode and cathode. Perhaps a laser could light up the surface of the anode at the exact energy needed to free electrons, I dunno. But I wonder if he's planning to do something similar:

https://www.youtube.com/watch?v=YFkUOPl0tUw

Another problem is that the ions move incredibly fast, potentially faster than the speed of sound, but only drag on the order of 1 in 100 other air molecules with them. It quickly saturates so a linear increase in current gets a sublinear increase in thrust. So an EHD engine is more efficient at lower speed, just like a helicopter prop. That's where creating more ions with more surface area might help. Also pulsed DC might get good airflow with fewer ions, so far the best result I've seen is 886 W/kg, similar to a helicopter:

http://jnaudin.free.fr/html/lftphv.htm

At the end of the day, EHD engines will probably end up working more like drones and balloons than rockets. Although some people have messed with putting the anode in front of a wing for a bit better lift.

Anyway, this is all great and stuff, but people like us on HN are relentless hackers. If I was part of a think tank and found the resources to fund it, I would take these experiments to the limit and build the best possible EHD engine. Maybe try to get to 100 W/kg to start, then shoot for 10, and so on. Which is why I think the Skunk Works or DARPA or someone like that probably built one back in say the 1960s and kept it secret:

https://en.wikipedia.org/wiki/Biefeld–Brown_effect

JP Aerospace was going to build an airship to orbit with their Ascender model, powered by an EHD mesh in front of perhaps an aluminized mylar balloon/cathode:

http://www.jpaerospace.com

That's the only real threat to someone like SpaceX that I know of. Their idea could work, although I suspect that thrust reduces proportionately to the air thinning with altitude. So they'll need a way to gather a larger volume of ions in front of the ship, maybe with a laser or something magnetic, as you suggested.

It would be like building an airfoil 100 times more efficient that anything we have now, so that it could fly at 100,000+ feet (20 miles) at 1/100 atmospheres of pressure the way an airplane flies at sea level. Then gradually ascend to perhaps the Karman line at 100 km (60 miles) by changing the geometry of the airship to fly faster or just use rockets like an RDE or something.