This is going to be long I'm afraid but read through it as there are suggestions in there among the background info.
Well done on checking those test points. That sounds pretty much ok doesn't it? At 29/30mV that means about 19mA bias current (across 1R5 resistor) which is well in the ballpark for an EL84. The HT is 390V and maximum anode dissipation for the EL84 is 12W. That means a maximum current of 30.7mA. As a rough guide 70% of that is 21.5mA. H&K's setting of 19mA is 63% and is pretty much spot on for sensible reliable valve life.
Incidentally as a general rule for your future valve amp work, the "70% rule" for "best" bias is followed far too slavishly by a lot of people who don't really understand how variable everything is in this area. Accuracy of 1% is ridiculous in the context of any guitar amp output stage. As long as you don't exceed that or drop too low below say 60% things will be fine and you will hear very little difference except at low levels. Crossover distortion, which bias is there to minimise, stays roughly constant as signal level changes so it actually increases as a percentage as signal drops. That is why amps often sound VERY rough when you bring them down to very very low levels. You can often actually hear the really grainy quality of the crossover distortion coming through. If you are ever working on a manually tweakable amp just use your ears and be pragmatic, drop the bias until you can hear a difference at playable levels and tweak a tiny bit above that. Playing around with it with a meter to fine tune it to 70% to the Nth degree is a sure way to put yourself into the mindset that you SHOULD hear a difference between 30mA and 30.5mA - so you DO hear a difference even though it's not there. And then you are right on the edge if other factors are leaning the wrong way. Remember, many things in a valve amp drift over time. There is a huge amount of this problem in many areas of guitar amp work. "Perfection is the enemy of good!" Just go for what sounds good without looking for what could - just - might - possibly - "someone said online" - be a shade better.
If the bias setup isn't the problem which seems the case then let's put this back to looking at other things. Another very real possibility which fits the symptoms is that you have a problem in the Power Soak circuitry. This comes after the power amp of course and, if it is not switching and selecting correctly, it could cause all of the symptoms you described in your first post. Check out the state of all 10 of the Power Soak resistors and the 4 inductor coils. They are the large power resistors mounted off the rearboard board in cutouts of the PCB for heat dispersal. As long as they look fresh and not heavily scorched they should be fine. I would have thought that the most likely culprit here is the switching relays. There are 3 of them labelled RL1-3 on either side of the Soak switches on the pcb. They can be accessed on the back side of the PCB without removing any of the boards from the chassis.
Each relay will have 6 pins in a square close to each other and 2 pins further away from them. This is a 24V relay with what seems to be a standard relay footprint. BEWARE: These relays are classed as 12 pin packages - BY H&K. Other relay manufacturers like Omron number their pins differently with 16 pins. There may be differences between similar relays which mean they won't fit on the board. As far as H&K's numbering, imagine a row of 6 evenly spaced pins down each side. Pins 2, 6, 7 and 11 are not used in this footprint. They use pins 1 and 12 for the coil. The wipers of the two switches are on pins 4 and 9. These switch between pins 3 and 5 on one side and 8 and 10 on the other. Here is an example of the type, there are lots of manufacturers who make these, Chinese are reasonably good for general purpose use, and they shouldn't be expensive items as you can see.
Omcron Relay I have only posted this relay example to show what they look like as ours are very similar, the pin spacing is wrong for the H&K pcb but I can't find the correct type offhand. I'll keep looking. You can see the positions of those on the pcb in the picture I've posted. The resistors are of course the large ones immediately above their position.
The control system for the relays is not as you would expect, it isn't a straight "switch and activate" action on each one. The settings of the 4 switches generate an increasing DC voltage level which is then converted into the different control states via an ADC at the microprocessor. This is digitally processed (in some way which is hidden from us) and is then passed back out as a PWM voltage which is converted back to a DC voltage which in turn drives a ladder of opamp comparators each flipping high at a higher voltage. As the voltage climbs up to 5V each one switches in turn at 1V, 2V, 3V or 4V, (the lowest of those is a line back to the microprocessor). There is diode steering setup in there too so the relays don't just switch one after the other, the action is more complex as they will switch on and off in combinations. If you can I would just measure the voltage across their coils in turn for different selections of the switches and check that you can see these swap between something like +22V and -3V. Don't worry when they change.
Now is the rub. Even if you get the correct (or sensibly believable) voltages across those relay coils that doesn't prove the relays are working. It just rules out the control circuitry as the problem. The voltages would still be there even if a coil was burned out. Feed a small signal through the amp from your generator keeping the level low as it is only there to give you a visible indication on your scope at the output. You can then check whether each relay is passing it through its terminals as it should.
We are now looking at the other 6 pins of each relay which are the internal switches. The centre pin of each line of 3 is the wiper connected to either of the 2 outer pins depending on the state of the relay. I can tell you that RL1 and RL3 are just paralleled up, both of their internal switches are connected together across the lines of 3 pins to double the current capability. This makes them easier to check.
RL1 has the output of the amp fed to its wiper so that voltage should be passed through to the outer pins in turn, only one at a time of course.
RL2 is more complex. One switch wafer will have a signal on its wiper in only one state and nothing (it's grounded) the other. The other wiper will show signals in both states but they should be distinctly different levels.
RL3 is a bit simpler. It may show voltages on all 3 pins. One of the outer pins will show the same voltage as the wiper or no voltage, while the other pin will show the same voltage or a larger voltage.
That isn't as clear as I had hoped I might have made it but the action is quite involved. It isn't just normal Switch On/Switch Off relay action. I would start with the Power Soak as all of the symptoms could be caused by that being faulty. It should be easier than what you have already done as you can access what you need with the boards all in place. I hope this is going to give us something as the other possibility that comes to mind is - the Output Transformer. H&K only and they will only supply to their network of repair centres.
Anyway, how does all of this sound to you, is checking out those relays doable? Remember, THERE ARE STILL BIG VOLTAGES IN THERE. (I can't stress that enough.)