I think my corporation would be into bio and nano technology as its main push among other things.
I'd have to say a crude form of warp drives should probably be available for use in this scenario. Traveling to the next solar system over (4.3 light years) would take us tens of thousands to hundreds of thousands of years without a FTL drive. Now imagine something not so close. A crude warp drive might mean a trip to Earth takes a month or more, not generations. Also, inside a solar system maybe we can't use a warp drive but use a slower crude impulse drive better suited to flying in a solar system. This would allow days between planets or less rather than years.
Also I agree that any tech to be added to the Approved list needs to be shown to be Reasonable, Researched/In research, Probable in the allotted amount of time. (e.g. No 'Death Stars', Halo ring weapons, Star trek level teleporters, Synthetic wormhole creation, etc.)
If Syrixia gets lightsabers I am so going to be in on that one.
Regarding the map, I like the first draft, and offer suggestions for two objects on the map for v2:
THE BINARY:
Binary planet would be nearly next to each other on the map and are tidally locked objects. (Think the moon and earth but the moon is bigger and habitable.) I found a similar graphic to how this would look (minus their ring), but the planets would be about equal in size.
Also about this binary planet, they probably need a bit more space or they'll rip their neighbors a new one with their combined gravity.
Last is their orbital position is both eccentric and inclined similar in nature to our dwarf planet Eris. The binary would be a highly eccentric orbit starting in position 4 and continue near to the first belt (AB1 (Auxil)) where it refreshes its ring material. Example of an eccentric orbit:
This orbit would probably not adversely effect the other planets either as it crosses their orbits because of a highly inclined orbit. The inclined orbit is usually the result of large disruptions like the one that would have formed the binary. Here is an example of an inclined orbit:
The other planets would slip through the inside of the large binary orbit like rings inside a ring.
THE BELT (AB3 / Kesot):
The second suggestion is showing asteroid belt 3 just after the last planet and before melting into the unknown / dwarf planet territory.