Hey Tubes, here's a reply I started two nights ago but never posted:
A really handy book is the Audio Designer's Tube Register Vol.1. It's got plenty of characteristic tables for common 9-pin tubes, including when said tubes are used with a constant current sources. This book is the source for the data I'm referring to. One drawback of the 12BH7 vs 12AU7 is it's higher inter-electrode capacitance (grid-plate and grid-cathode). However, in a low-gain circuit such as a line stage this difference in C would not be too noticeable.
So basically, the rule of thumb is that a 12BH7 can be substituted for a 12AU7 but not the other way around, as the 12BH7 has a couple higher design-centered maximums that may be too much for an AU7, including the heater requirements (how a 12BH7 can operate on half it's required heater current and still sound good is a mystery to me). Otherwise, they are very similar.
The filament windings of the spec'd Clarinet transformer are rated at 2A and there's only four heaters in parallel; that's accounting for only 600mA of the 2000mA rating. So your question is "is it safe?" Yeah, from my experience it's safe. But will it sound as good or better? Maybe. Should the heater be optimized first? Probably. Can it be optimised? I dunno.