Hello franzik,
As what i understand the Bedini charging system is effective on battery only after many (Don't know exactly) cycle of charge and discharge.
Also you should't know that a voltmeter or multimeter is not the best device for make measure on Bedini output, because it's not designed for measure pulsed current or volt, the voltmeter show only "a part" of the oscillating values, let's see this screenshoot take on my system with 12 v supply and potentiometer @ 0 Ohm:

As you can see this is a pulsed tension, max pulse is between 45V to 100V maybe more and if you take measure with voltmeter it show 2,5 Vcc, that is the spectacular particularity

.
It's very interesting that it work on new lead acid, what is your voltage supply for charge them ?
For the 2N3055 problem i think that the best supply voltage is 12Vcc, with 24Vcc it's maybe too high and the pulsed peak too.
I hope help you,
See ya...