The custom game selection will allow you to draw from maps that you have uploaded to battlenet via the Galaxy Editor. As I understand it this is exactly what you want to do and it sounds like you do understand how to publish a map.
I believe there is an option to publish the map privately for custom game use, though I haven't check since Beta.
For the 'Kin' achievements i had a hard time until i ended up using silly tactics for each of the 3 races to allow my team the win with a lot more ease, and a lot less frustration at my idiotic teammates.
Protos
Cannon Rush. You can see my description of it here.
The basic gist is: send a starting probe to their base (on Megatron) and set up a pylon and forge, then start planting cannons until they are all hampered enough that your team rolls over them.
Zerg
Spine Crawler Rush.
This works best on maps where all the bases are seperated.
This means your opponents all need to be zerg.
Harvest for < 1min with all of your drones. Build 1 or 2 new drones. Then save up for a pool. After the min has past send 2-4 of your drones into the opponents base. Then split them up 2 per opponent base. As soon as you have the resources turn those drones into spine crawlers behind their resource line. Use the minerals to funnel the drones so only one can attack your spine at a time.
If all goes well you will land 2 crawlers behind 2 different bases and it will cause enough economic damage that the other 3 players on your team will be able to roll over the opposing AI. If all does not go well, they will have attacked your crawlers and killed them. Save yourself the time and pack up and surrender. Just try it again.
Terran
I chose Protoss for my opponents on this one.
This works best on maps where there are two players per base.
I built fast into 3 barracks with tech labs and mass produced Reapers.
I then proceed to reaper harass the opponents, watching for striders and zealots to come defend while cleaning house of probes. If you are able to take out a nexus early, that's always very helpful.
If all goes well you did enough damage that your buddies can clean house, otherwise start over.
Hope this helps out, this is exactly how I did them.
Best Answer
I believe that it does have to be a blizzard sponsored map. Easiest way to get it in this case is to play on Lava Flow as terran. As soon as the game starts, load your scvs into your command center and fly to one of the islands. Get an engineering bay pretty soon, and start to pump out turrents along the edges, and go strait to battle cruisers. Soon there will only be one AI left, and you should have close to 20 cruisers, so you should be able to steamroll.