I had looked into different ST-70 front-end here's what I have in my notes about the 12AU7 vs. the 12BH7.
The 12AU7/12BH7 has µ = 17, which is fine for the splitter but less fine for the gain stage. The ST-70 doesn't need huge amounts of gain, but a 12AT7 has µ = 60, for comparison.
The 12BH7 was designed for TV vertical deflection and oscillator circuits, and the -A version has some special heater warmup tweak. It reportedly can be noisy in audio use, probably from heater to cathode leakage. The 12BH7 draws twice the current draw of a 12AU7, 0.6 mA instead of the usual 0.3 mA, but that shouldn't be a problem for your power supply unless it is at its limits.
You might have a bad tube, a version prone to noise, or idiosyncratic wiring issue with an AC imbalance that causes the tube to hum.