For the sake of understanding why you're experiencing high levels of frustration, are you able to list the OXP's you are using. It's certainly possibly one or two of them might be contributing to the numbers of pirates you're seeing. (One question - 6 pirates usually means 6 lasers. Only OXP ships have 2 lasers mounted up front (Cat Mark 2 and Iguana if I recall correctly), both of which are OXP ships, and both of which are known to be a real pain to deal with regardless of what ship you're flying.)
FWIW, I'm using over two hundred OXP's, and I'm flying a standard Iron-Assed Cobra Mark III. Just yesterday I was jumped by 8 pirates and managed to kill them all. I am, however, using a joystick (a Logitech F310
... cheapest new joystick I could find!). My tactics are to inject into the middle or the rear of the pack, making sure they stay as bunched up as possible. Then I start picking off ships. In close quarters the pirates can struggle to get a hit on you if you make sure you don't fly in a straight line for too long, and watch out for ships that have a rear laser mounted. I find some pirates tend to fly straight when you're attacking from the rear, meaning you need to watch your 6 and start moving around to stop your rear shield from being shredded.
I find ECM missiles can be useful for two things. First, they can finish off ships that don't have injectors. Second, if I need to reduce the number of ships I'm dealing with, I can target a ship I know will probably have injectors (eg most Asp's), and then fire an ECM missile at them. They will quickly inject away, giving me more time to deal with the other ship before the Asp returns to the fight. It's still possible to hit ships that have injectors with ECM's, but you need to be quite close behind them.
Bad things to do: go head to head with ships that have missiles (FdLs, Asps, Pythons, even Adders). If you start laying into them with your laser it's quite likely they will fire a missile at you pretty much point blank. Always get behind a ship before you start dismembering them.
[shameless plug mode-on]You could also try using Broadcast Comms MFD. This OXP gives you the opportunity to try and bribe your way out of a battle.[shameless plug mode-off]
I can't say I've tried flying an Andromeda before. I've loaded one up for testing my OXP's, but haven't tried it in combat so I don't know what it's maneuverability is like. From the Wiki I imagine it's more towards the "slow and ponderous" end of the scale rather than the "can turn on a dime" end. Tactics when flying slow ships are different, so perhaps someone with more experience with large ships can chime in with their thoughts.
Edit: Also, can you describe the config of your Andromeda? ie What lasers you're using, what equipment you have installed, that sort of thing.