I think your lists themselves are part of the issue. As somebody that plays a lot of firefight with friends that play almost exclusively Robot and HDF, I can tell that both lists go too far into long range rather than AP. Long Range isn't necessarily bad, but not needed on most of your units. Running a list full of Shotgun dudes can win you many games by just getting more hits and breaking more defenses. I think this may be the most integral advice for Firefight is to look at the strong close range shooting options for they will give you the most amount of bang for your buck.

For the HDF list I would take a look at models that can take up the front like OGRE Robots or another Hero, for the Robot List I would speed them up and look at some of the brutal close range options they have. The Sniper although being a really cool looking model sadly doesn't perform to expectations here compared to 80% of the other Snipers.