What you're describing is basically how the APFSDS-T (also called, among other things, a sabot)projectiles work. They are sub-caliber projectiles, made from very dense and heavy material (depleted uranium, tungsten etc), which travel at high velocities to achieve kinetic kill.
Current variants do reach 1.8 km/s, as you mentioned. This allows them to achieve successful penetration of (at minimum) 850mm of RHA armor. That is a lot, but new ones, entering service now, have much more penetration. How much is yet unknown - numbers are unavailable. But they do it in one of two ways: increase velocity at the moment of strike and/or increase mass of the penetrator.
There are in development new types, where the increase is in speed. It is estimated that with all other factors staying the same, increase of velocity from current 1.6 km/s-1.8 km/s to desired 2 km/s adds a bit over 10% to penetration values. Though it may require different material of the penetrator. There's a reason why US is sticking with depleted uranium penetrator - where velocity is actually lowered, but mass is doubled, and ERA-defeating capabilities have been added... It has been found that there is a point where too fast is actually a thing.
So, if you plan to go up to 4 km/s of penetrator velocity, it means that this projectile will have anything between 2x and 10x increased lethality compared to defenders. Depending on the end of that scale it will at be at least enough or way more than enough, then. For example, latest US APFSDS produce on impact almost 11MJ of kinetic energy from 10.5 kg penetrator at 1.65 km/s velocity. If same projectile would travel at 4 km/s, then the energy yield is just around 80MJ. For comparison, 155mm HE projectile from current-tech howitzer explodes with about 55MJ of energy (though from 10.8 kg of TNT explosion), and it has been demonstrated that it will basically crush an M1 Abrams tank no problem. What an 80MJ kinetic penetrator does to a tank is pretty much the same, just bigger still.
Current defensive tech is basically what you described, as well: don't get hit. Of course, there are additions, like composite armor, reactive armor, shape of the armor (sloping and angling to increase chances of projectile bounce), which increase survivability - and it is worth noting that explosive reactive armor (ERA), while developed against high-explosive-anti-tank (HEAT) rounds, can be quite effective against some of the sabot penetrators (i.e. Kontakt-5 ERA uses the brittleness and rigidity of tungsten against itself, in effect shattering the penetrator and rendering it useless) but the tactics are basically shoot and scoot.
So if you look for something to increase survivability in the face of enemy with superior firepower you have two ways, one of which you already discarded (add more armor).
That leaves the other way: stealth. Make your vehicles smaller, add some stealth tech to them and basically adopt tank destroyers tactics across the board. Which is basically concentrated fire from ambush, and then retreat.
Alternatively, if enemy uses mostly kinetic-based firepower, then consider producing man-portable weapons and/or technicals in large numbers (where platform is civilian-market vehicle with added gun). Because in this case no armor is the best armor...