I'm fairly certain this is actually a bug. In Flash, buying Advanced Crew Quarters increases effective Crew capacity by 1. In JavaScript, it increases effective capacity by 2.
Just remember the Sidewinder has no weapons by default.
If you're recruiting Crew members as you go along (rather than waiting until after Zheng Shi), you'll run out of space fairly quickly. Unless you turn on Unlimited Crew Cheat.
Used to be that better ships had more Storage capacity. Z14 had 10/Category, highest was Clydesdale at 50. For whatever reason, all ships now have 30. Which does disincentivize upgrading.
I was able to beat the (optional) fight to enter Zheng Shi with a stock MS-XI. You're saying the Casstech Z14 can, too?
Generally speaking, I only ever pick up Yammi, Ramis (because they're basically the NT gym inside of your ship), Kase (who doesn't save a cute catboy from abusive corporations owned by the rival?), Anno (the
best girl), and when I get Uveto unlocked for a little extra space, Azra and Mitzi because I don't get any other characters joining my ship until far into the late game. If I ended up spending more time on Tavros, I would probably swap out Azra when the advanced quarters bug is fixed, after I'm done with her content since she still only has Mhen'ga and Tarkus.
And you actually can beat the optional Zheng Shi fight with Casstech Z14. With a couple Shield Boosters, a ship upgrade to increase Power Generation, reading the text, having high stats (use Yammi and Ramis to grind Reflexes [also adds Willpower] and Physique, Mhen'ga Syri to grind INT, and use stat boost from leveling up to max out aim. Wait for 5 minutes to remove a level of soreness.) and immediately targeting the EM turrets, you can slowly yet surely pick off the two ships you have to fight.
Although the battle will be slow and you have to watch the enemies' energy levels, the chances of losing with the Z14 with only a 15K credit minimum upgrade is so small, it might as well be smaller than whoever has the smallest dick in the TITS universe. Each shield booster gives 4000 in shields, and that's quite literally the entirety of the Casstech's shields. Evade when they are able to fire their thermal projectors,
which means you should evade the first 3 rounds of combat, fire when they're using machine guns/recharging, and recharge only if they're doing so too and you happen to be low. The fight is incredibly easy, and you'll hardly come out with more than a few scratches, but nothing too bad for your next pirate encounter atm as you should be able to escape easily regardless, or beat down the next corona lord. Don't be afraid to lose a little armor, as your ship's shields can never be permanently weakened/disabled atm, and will always come back after every battle.
Before the end of every single one of my playthroughs, which is before I get Sidewinder as at this point I already have my stats maxed along with some of the most OP weaponry and a fortune in harvested credits from Zheng Shi, my upgraded Casstech effectively has 9,000-12,000 shield points assuming relatively perfect shield boosts, 35 power generation, and 6 crewmate spaces, 5 if that bit about the bug is true (which I do believe, the desktop version I have doesn't add +2 to crewmate space, only +1.). And either way, I can just leave Mitzi on Tavros without any consequences; it's even in my benefit if I leave her with Bizzy. Sometimes, I'll actually even get to Zheng Shi before ever visiting Tavros a second time, so I never have crew space problems.