With a 15-minute defender mode game, I'd suggest using the largest map your computer can handle and taking as many worlds to start with as possible, upgrade the metal and crystal harvesters to mark III, and set multiple planets to repeat-build every combat ship you can. I'd also suggest doing this on an easily choke-pointed map (like X or Snake), and making certain the AI can only reach you at one or two worlds.
Immediately start building a fortress world at a decent chokepoint (not one of the worlds right next to the AI homeworlds - those will fall with the first wave - but rather one four or five worlds farther back). X might be a better map choice than Snake, as there are worlds that the AI might divert ships to that are more or less dead ends. Preferably, most or all of the worlds you have building ships will be streaming ships either to or through the fortress world, and will not be closer to the AI than the fortress world.
Warning: I tried this once on a 120-planet X map, where I held 118 worlds. The first wave contained more than 50,000 ships, and by the second or third wave the game was running so slowly that I abandoned the attempt. However, if your computer can handle a 120-world 15-minute defender mode game where you start with 118 of the planets, it is possible that all you would need to do is wait for the countdown to end, because the AI might not be able to hit all 118 worlds in 15 minutes.
I would also agree with Hearteater that, in Defender mode, you really do need to have more than one home planet, and a 10-planet map is probably way too small for high-difficulty defender games, because even if you take the 8 planets you're allowed to have, the AI has a decent chance of overrunning every world you own with its first wave (in the game I mentioned above, the AI's first wave took the border world, and then proceeded to overwhelm the three neighboring dead-end worlds and start on one of the worlds leading towards my fortress world by the time the second wave was announced - this despite delays caused to AI fleet movements by ships that I'd set to constantly build and immediately send in free-roaming defender mode to the border world - and by delays, I mean the AI fleet went 'Oh look, another ship to kill - let's lay waste to it with this whole part of the fleet').
