I think more lights are better.
There is a way to make them both running and brake lights with only 2 wires. (not knowing what the mini controller you mentioned does.)
You'd need to buy a resistor and 2 diodes.
The resistor would go before one diode and attached to a feed coming from the running lights. This would cause the lights to be dimmer (if the resistance is too high and the lamps LED they would not light) The other diode would attach to the brake light feed. The diodes are there to allow the power to run one way only and prevent the power from back feeding to the light.
You could also buy a trailer wire adapter unit that that allows use as direction signals. Just wire the "to car" to the feed from the bike's lights and the "to trailer" to the LED's in the top case.

Now depending on where the flasher is for the lights will determine where you insert it. Usually the flasher would go before the brake diode if you didn't have the direction signal add-on, or before the trailer unit on the direction signal add-on.
If you did BOTH then you'd need an extra diode and resistor. The "to trailer stop and turn" would run into a "Y resistor diode" for each side. The "running light" feed would be split and hooked to each side. Confused? It would look like this (bad diagram to follow - flasher unit not shown

)
I assume you have 2 separate flashing systems based on the video. The lights being out of sync, while great for being seen, would be my only concern with the law enforcement officers giving you a hard time. To me it almost looks like wigwags vs just a modulator/flasher. If it was me I'd have them in sync but that's my OCD
Now if the mini controller does brake/tail or brake/tail/turn signals in one box, then it should be a whole lot easier for you as it does all the above in one pre-built box.
(you may be even able to buy a prebuilt unit on Amazon / eBay etc.)