The Antimatters might be useful, but they'd be the entire fleet due to the early economy. I'd have nothing that countered the smaller stuff. Snipers are great but they're so crystal heavy they can erase an economy on their own.
This is true; I'd been thinking that the 8x HW economy would give you what you needed, but yea, you've got 8x to build too. The early-game economy is wayyyyy faster than it used to be many versions ago, but it is definitely finite.
However, to gateraid I need to spend some of the resources in an attack posture which lessens what I have available for the raid.
If it's not covered by a forcefield you can gank the warp-gate itself with a fairly small suicide force. So resources, but not as much as you may think.
Alternatively you can turn on cpa-like-waves (it might be called cross-planet-waves in the lobby) which will basically make it always spawn waves like you'd gateraided your entire perimeter. This generally makes the game harder (massive threatball buildup, I've noticed), but if your focused goal is surviving the first wave...
Also, as I think one of other posts was talking about, AI threat ships can be "persuaded" to wait on the other side of the wormhole if they think you've got enough firepower on your side. That could give you the time you need.
and it also increase the wave size by 50% (10 AIP to 15 AIP)
In the very early game that's actually not true:
http://arcengames.com/mediawiki/index.php?title=AI_War_-_Why_Do_Enemy_Waves_Get_So_Large%3F#How_Wave_Sizes_Are_CalculatedSpecifically, step 3 means that the actual individual wave sizes will be the same until you hit a certain AIP value (depending on difficulty). There's also a degree of randomization in step 2, but that's largely diluted by the fact that you have 16 waves coming in (ouch!).
On Diff 10 the base size from step 1 is: AIProgress * 3.33~ and the floor in step 3 is 100. Therefore you have to hit 30 AIP before wave sizes start to increase at all. 31 or 32, really.
Another thing to factor in to finding some solution,
any solution to this is step 4: different AI types use different wave sizes. If you play against 2 mad bombers then just forget it, as that doubles wave sizes right there (not to mention that those have a high chance of tossing a bomber starship into waves). To assist, I expanded step 4 to include a table of current multipliers. There are other AI-Type-related factors that play into the "defensive level" of planets and whatnot (whether a planet gets a fortress, how big of a fortress, etc) but those don't directly relate to the wave size question.
Another thought is that the wave AI isn't the smartest: you may be able to distract it by keeping it running around on a nearby AI world (assuming you've gateraided and the wave is coming in from a further out planet) to buy time or at least split it up. Keeping your distraction forces alive long enough is left as an exercise to the reader.
Although i am not sure if unit caps affect how many units a tractor can affect
Tractor turrets have scaling caps too, so even if the enemy has 2x as many fleetships, you have 2x as many tractor turrets, so you're even. The Riot-starship based tractor modules do not scale, though, so they are more useful on low than on high; I intend to fix that but it's not a top priority.