Why does my 35 watt tube amp draw 300 watts of power

More than likely it only draws 300 watts at full power output. Probably a lot less at idle and playing at moderate levels.

Power efficiency (and excess heat) was a concern of mine when I ran just solid state gear, but since I became hooked on tube gear  ...well, if inefficiency is the price for this kind of a wonderful listening experience I'M ALL IN!

But, this comes at a price —not just heat but time to warm up and "disposable" tubes if you listen for hours on end and do so day-after-day. For serious listening: Tube gear. For convenience: something solid state. 

I have a Dialogue premium HP, 85-90W/channel and 540 Watts consumption (max.)  Like you said, love it, not going back to Solid State.

Cost wise, running the amp at full consumption for 2 hours each day costs $.09/day or about $3/month.  In reality probably only using 200W max, so we are talking about another $1-2 per month in expense, $5 if it runs for 4-5 hrs each day.