There is no displayed countdown, but it’s something like five or ten minutes with no hits aside from “reflected by shields/armor”. A good rule of thumb is if the battle’s drawn out long enough for it to become boring, it’s time to hit the retreat button (unless you are winning, in which case it’s time to go do something else like read a book for a while and hope the draw breaker decides in your favor).
I also don’t know where you’d find the time-out setting to change it, or even if it can be changed.
I’m a bit surprised that the cruiser with three ultraheavy armor plates was capable of resisting heavy cruiser plasma. Did it by any chance have other armor plates as well? Most useful designs for cruisers won’t be able to survive hits from heavy plasma if all they carry is three armor plates.
As for highest armor penetration - that goes to the Cruiser Proton Beam (73); next is the Cruiser Beam Laser (70). Heavy Plasma Launchers are down at 55, which is higher than most weapons but far from the highest penetration. They do however have one of the highest shield penetration ratings (also 55, unless I’m mistaken), but differences in shield penetration value are meaningless if they are all greater than 27 (highest shield resistance outside of mods).
If you want to keep using cruiser plasma as your primary weapon, it might be good to have one or two Cruiser Beam Lasers or Proton Beams mounted in the furthest-forward turret position for armor-breaking purposes (you don’t necessarily need these on every ship, just on the ones closest to the head of your formation, but in campaign I prefer to have one proton beam on every ship in case of losses if I do this kind of strategy). You will still come across a few ships that are essentially immune to your fire, but it takes a lot more effort to grant immunity to proton beams than to cruiser plasmas, and that greater effort costs the ship much of its potential firepower and often its shields.
Large fighter swarms (using fighter lasers or fighter pulse lasers, depending on your preference and what you need to do to enemy fighters) can also be used to somewhat rapidly break armor, especially when they are supported by a cruiser mounting a Proton Beam or other high armor penetration weapon. Pulse lasers work better for strafing cruisers and frigates, while laser cannons work better for dogfighting; additionally, pulse laser-armed fighters will generally take heavier losses than laser fighters will. Fighter rockets can also work for this, but cannot be fired from under any normal cruiser’s shields. If you do go in for pulse laser or laser cannon armed strafing squadrons, set their ‘engage cruisers’ and ‘engage frigates’ range to the minimum, since that should make it more likely for them to pass beneath the cruiser or frigate shield bubble to take out some of the armor before the shields are down.
Note that in the campaign it is also possible to achieve a critical mass of fighters, which will result in your cruisers essentially not contributing to the battle because you have so many fighters that enemy ships simply die before the cruisers can do much. Just be aware that fighter swarms are vulnerable to better fighter swarms and good fighter defense, or to fleets that have the ability to rapidly kill your own cruisers and frigates and kill enough fighters to win with the double-enemy-strength against fighters win condition.