Roll 7 to 9 dice at once, color-coded.
I typically roll all the likely-needed dice at once for an attack, split up by color.
- 3 green dice for the attack roll.
- 3 yellow dice for the defense roll.
- X dice for the damage roll, according to the weapon damage.
That lets me quickly roll and read the result, rather than taking time for each step. If the attack misses or the defense succeeds, ignore the other dice. As a bonus, if the red dice read high, I can add some color description like "Karl takes a swing that would surely kill you, but you barely deflect it."
I roll the dice into a space on the table with barriers, so I don't have to chase after dice, etc.
Of course, some players prefer to roll their own dice, so I ask what they prefer. For NPC vs. NPC rolls, the full pool can still be rolled by the GM. If a player is involved in a roll, and they want to roll, the GM can also roll the NPC dice at nearly the same time - just the habit of thinking of combat action/defense/damage as being calculated quickly together can be useful to develop GM habits that allow quick resolution and narration even when the PCs are rolling, as opposed to thinking of each step at involving time to consider, choose, look up numbers, and roll.
Also, I tend to require players to be ready to declare their action when it is their turn. I tell them to think about what they will do in advance, so they have an answer ready. Too much delay and their character takes a default action appropriate to the character. After all, turns are one second long. It's entirely realistic for many/most characters to spend many/most turns not doing anything useful, let alone brilliant and well-considered. Certainly no looking up of rules.
And of course, I have all the usual needed stats for everyone pre-calculated and listed so they are very easy to read, so I almost never need to take time to look up what someone's skill is, or if I do, it's right there. See the GM Control Sheet. I make those for NPC groups too.
Also, I've been playing GURPS forever and I'm very good at math and reading die rolls, so it goes really quickly for me. It took a year or so before I got really fast at it. But once I've memorized most of the rules, combat doesn't take much longer than the rolls, and by combining 3 rolls into one, it really speeds things up.
(I'm also really interested in combat, so I actually enjoy the time I'm resolving combat.)
Don't fight to the bitter end.
Consider the situation for everyone in combat, and consider they probably really want to survive. When a fight starts to not go their way, roleplay what they do about that, including negotiating an end to the fight, running away, surrendering, playing dead, not getting up after taking a wound, calling for a retreat for their whole side, etc.
That can be good in other ways, too, as surviving opponents make for a more interesting ongoing situation, and the possibilities of surrender and negotiation, or capture and ransom, can all be quite interesting. They make the game more humane and real, and it also can be much more nice and interesting for the players if they ever lose a battle, to have not fighting to the death and being slaughtered a reasonable option.
If you and your players really don't care much about combat details, then consider optional rules to abstract things.
One such is any of various optional rules where the skill and defense levels of both sides can be reduced by skill, or the degree of success on an attack reduces the defense, or an attack is handled as a quick contest of skill.
Heavy armor has various counters.
As for armor, the values are meant to be semi-realistic, and if anything they're actually pretty low compared to the protective value of real armor.
I don't know at what level you want to address the issue of armor, but there are several ways to get more injury at TL3:
Set games where there aren't many people in plate armor. Only late-medieval TL3 really historically had much if any plate armor. Hot climates tend to discourage heavy armor. Sailors tend not to want to risk wearing heavy armor. Etc.
Use deadlier weapons. Heavier weapons, finer weapons, weapons wielded with more strength, magic weapons.
Use a culture where many fights are to first blood.
Check out the rules for aimed shots. Several target areas can take someone out of combat with not that much penetrating damage. Same for targeting weak points in armor.
Note the rules for knocking people down.
See the rules on disarming people and breaking weapons and shields.
Use the optional rules for standing up in armor. Not only does it discourage wearing very heavy armor, but those who do can be subdued by knocking them down and then dealing with them while they are down.