How did you manage to conquer those markets so early in game, can you elaborate a bit more? I'm interested in trying it out myself.
Starting skills: Ordnance Expertise 10, Damage Control 5 (Or Evasive Action 5), Helmanship 10, Power Grid Modulation 10.
Bought 90 marines and a Mercury shuttle from Jangala, you could buy way less but it doesn't matter since it's your only expense atm (and you start w/ 250k credits).
You should only encounter the response fleets when attempting to capture the markets, though that shouldn't be a worry since you will be hopelessly outnumbered anyway - and yes, you can slug these out before your CR timer runs down w/o Hardened Subsystems.
Deploy the Eagle only, and hold postition. When the enemy starts pouring in, backpedal to the edge of the battlespace (take care not to retreat from the battle itself, and make sure you start pulling back before you get swarmed).
(Ideally, retreat to a corner of the map, but I've just reversed straight to the bottom and it worked for me. Pirates are very weak after all.)
This should severely limit the number of enemies that attack you at once, thus making it easier to slug it out. Just don't forget to prioritize fighters and bombers i.e. you should always take them down before they have a chance to unload their ordnance. If you have Evasive Action 5 and a Reaper salvo is underway you can easily fire up Maneuvering Jets, dodge two and soak up/shoot down the last one.
After this I've also captured Jameson Orbital from the JP/ASP/PACK mod, so I can have proper military fleets. Currently bounty hunting and trying to decide which faction I should join.