I have the same problem sometimes and still haven't found a reliable way around it that doesn't rely on ship specialities. What can help is using a bomb weapon to disable their weapons while you are trying to run away (even the small bomb available at the start will do). You could also try upgrading your engines beyond what you can normally power in battle, and then disabling everything that isn't essential in running away (even oxygen if you need to) and diverting that power to the engines so you can run away faster.
While I remember, I must warn you not to use the federation layout A ship. there is a bug where all the mini bosses are friendly, preventing you from getting the advanced tech. The layout B ship (Nisos?) is fine.
I've only done two major runs on infinite space, both stopped by the game crashing and losing my save file

Although I did have stupidly good ships that could blast through the mini bosses quite easily by the time it crashed so I suppose there wasn't much left to do.
On the first run I used the mantis layout 2 ship because it has a 4 man teleporter, took the small bomb as my starting gift and upgraded my shields to level 3. If i felt i could take the crew down i would bomb the medi bay fight them, knowing my shields could keep the ship alive long enough. If i didnt think i could kill the crew i would bomb the weapons and get out of there as quick as possible, praying the shield was enough.
On my other run I used the federation layout 2 ship and put the starting money into the shields and the artillery beam. If I came up against a big ship I would put as much power into shields, engines and the artillery beam as I could, relying on that beams shield piercing to kill the enemy ship, or bailing if I couldn't take the damage.
Does anyone know of a good save backup mod? I would like some way of getting my stuff back when the game crashes