Sure.
I have done it using materials other than lead with less density and as a result lighter. Such as all copper bullets, similar to the barnes copper solids.
The problem is the lighter you go the more the short barrel hinders potential.
A projectile that light needs a longer barrel.
Think in terms of acceleration. The less time the projectile is spending in the barrel, the less time it has that pressure applying acceleration. So a heavier bullet gets more time with that 37,000+ PSI than one that left the barrel sooner. This results in a curve that favors a certain bullet weight window for optimal power gains.
The velocity gains as you go lighter within that window can be substantial, but beyond it become minimal.
So a G20 and 6 inch barrel actually will come closer to what you want. (Or if you can get longer than standard aftermarket G29 barrels in 9x25dillon.)
In the heavier loads you lose a lot less from a shorter barrel compared to longer barrels. So as you go lighter the performance difference between barrel lengths increases.
There is diminishing returns in velocity gains as you drop the projectile weight with such short barrels. Beyond a point you gain little feet per second for the power you gave up.
Additionally the lighter the projectile for the pressure you are operating at the louder the gun. Those would deafen you very quickly from an under 4" barrel, even with minimal protection like ear plugs.
Such a round would actually be better in a SMG type platform with at least an 8" barrel.
There is some ways around the limitations to an extent, like using sabot rounds. But these will be complex and harder to reliably use with an autoloader. The benefit of the sabot is you can get the increased surface area behind the bullet, which gives more surface area for the pressure to work on. For example 37,000 PSI in a .22 barrel creates less energy than in a .40 barrel. So if you were launching a .22 projectile from a sabot in a .40 barrel you can achieve more energy than from the .22 barrel with the same pressure.
Likewise the 10mm barrel using sabots to launch 9mm or even .22 bullets (the 5.7 is a .22 and you have a lot more case capacity with the 10mm.)
Being that the 9x25 dillon is a 10mm auto necked down to 9mm, if you just use a 10mm barrel and run sabots to shoot 9mm you can gain more perfomance (though likely at the cost of accuracy.)