Just a few quick comments. First, you mention in your original post that you grab a few planets and develop them and build a fleet as possible. The balance between planetary development, research and fleet building in the early game is a delicate one, so it is possible that you have been putting too many resources into economic development, planetary upgrades and/or research, and not enough into fleet development.
The second thing that I will note is that you do not mention planetary defenses. Even if you don't build starbases right away, a couple of "turrets" are relatively low cost and will give your smaller fleet something to shelter behind when under attack by a larger fleet. A human player might well ignore them, but the AI will not, and they can soak up a fair amount of damage giving you time to eliminate the AI's supporting ships and shift the balance in the battle. You can also use repair platforms to create a more robust defensive zone, and if you hold your fleet in that area and the AI comes to you, you can definitely defeat a larger enemy. You can also build additional defenses in the middle of a battle, which will further distract the AI and give you more time to bring in reinforcements.
Finally, during all of this your expansion should not stop, either. Grabbing an additional planet or two can lengthen your chain of trade ports and boost your income at a critical juncture.
Hope this helps. Would be interested to hear more about your experiments/experience.