You've got good points, and I fear that the only way to really get an idea as to how powerful these cards are would be to actually play with them. However, given how many ways there are to damage starships, I don't think they'd stay around very long against an opponent determined to get rid of them. I gave Chewie an exertion cost and added a restriction to the Turrets.
Here is another batch of starship cards, this time Imperial!

Imperial Ace [Imperial]
Minion * Clone
Strength 9
Vitality 2
Site Number 4
Skirmish: Remove 2 power tokens from your [Imperial] fighters to make this minion
damage +1.2R29
Basic utility minion. Rare but weak, which is common of early sets.

Imperial Star Destroyer [Imperial]
Starship * Capital
Power 6. To play, discard an [Imperial] minion.
Weapons (Power 2): Damage an opponent's capital starship.
Weapons (Power 4): Damage an opponent's starship.
2U35
What I want from capital starships is a difficulty dealing with fighters, which I've captured fairly well here. Also, given that this has got 6 power, I don't need to give it a Shields power - it has built-in resistance to damage.

Imperial Wingman [Imperial]
Minion * Clone
Strength 6
Vitality 2
Site Number 4
For each [Imperial] fighter you can spot, this minion is strength +1.
2C36

Landing Shuttle [Imperial]
Starship * Shuttle
Power 3. To play, spot 2 [Imperial] minions.
Speed (Power 2): If the Alliance moves during the regroup phase, play an [Imperial] Clone from your discard pile; its credit cost is -2.
2U37
Keep in mind that having leftover power by the regroup phase can be difficult (I think), so I want something good in such a situation. But let's be realistic here, this card is pretty worthless!

Overwhelmed [Imperial]
Event * Skirmish
Exert an [Imperial] Clone and spot an [Imperial] starship to make a companion it is skirmishing strength -3.
2U40

Short-range Fighters [Imperial]
Event * Shadow
Spot an [Imperial] minion to play an [Imperial] fighter from your discard pile..
2C42
Gotta have a card like this.

Tallon Roll [Imperial]
Event * Maneuver
Exert an [Imperial] Clone and spot an [Imperial] fighter to discard a possession attached to an Alliance starship.
1C48
I really like the utility cards like this that have so many functions. Falcon's Turrets giving you trouble? That Targeting Computer scaring you? Tallon Roll it!

TIE Fighter [Imperial]
Starship * Fighter
Power 2. (At the start of your turn, reset this starship to having 2 power tokens. If this starship has no power tokens on it, discard it.)Weapons (Power 1): Discard an [Imperial] card from hand to damage an opponent's starship.
2C49
At first I gave the TIE Fighter power 1, but I realized immediately how useless it would be, so I think 2 is the minimum that a starship can really have. And since these fighters have gotta be weak, I gave it another cost to use its weapons.

TIE Scout [Imperial]
Starship * Fighter
Power 2.
Speed (Power 1): At the start of the maneuver phase, spot 2 [Imperial] minions to add

.
2C50
Basic basic basic!

TIE Wing [Imperial]
Event * Skirmish
Make an [Imperial] Clone strength +1 for each [Imperial] fighter you can spot (limit +5).
2R51
And yet another vanilla strength pump. To tell you the truth, I like this simpler cards, but I look forward to writing cards a few blocks down the road, where I'll get to come up with all kinds of zany rules that require lines and lines of text on common cards. But these early cards are fun too!