I'm not seeing the strategic reserve going after me anywhere else, but now and then I do see part of it transiting between AI systems.
If you see it transiting between systems, then it is the special forces. There's no announcement for those (Unless you've set up planetary alerts), and they are always in place on the map, while the strategic reserves have an announcement in the top left, and leave the map after they're no longer in demand.
The special forces are a lot easier to ambush. You can draw them to the site of an advanced factory, fabricator, core shield generator, etc under AI control, and they'll generally respond en masse. You can even hunt them down at their rallying point.
I'll load up that save later today (6-10 hours), and see how they're split up. I expect the strategic reserve is the main concern, but if the patrol is relevant I'll dish out a few tips on finding it and killing it. You may even be able to do that without warheads, but those sure are fun help.
Kahuna save, not OP save, nvm.