Wouldn't the BK-37 barely be pushing into those >2600 fps velocities at close range? The MK 103 pushed it a bit further though. The likes of the British Vickers S (Littlejohn ammo aside) were well below that, though not all that great for penetration given the 40 mm caliber. (perhaps still a decent trade-off for the germans with their shortages, especially if they'd developed a relatively light low/medium velocity Oerlikon/MK 108 style API blowback weapon in the 37-40 mm range and still push better RoF and velocity than the <2000 fps of typical Vickers S AP shot or at least be lighter, faster firing, and have smoother recoil)
I know there were some experimental light AP shot designs tested on the MK 108, but the loadings of that gun just seem too light to make that worthwhile.
Aside from that, if they were mostly using conventional heat treated high carbon steel for steel AP cores, there should have been some room for imporvement using higher strength alloys. Sure, those would include other strategically limited metals (chromium, molybdenum, vanadium), but it shouldn't be nearly as bad as using tungsten carbide. (and in fact, it would be similar to the high speed tool steels used for machining that might replace the superior carbide bits due to shortages)