You asked a number of questions, let me try to answer them in order.
1) They are design center values. To use your example, hammond winds the B+ (HT) secondary winding to give you 660Vct at 138ma while living within their own specs (e.g. the transformer temperature rise will not go above some safe value, and you can run it like that all day long. It also considers the size of the wire to not overheat due to current draw, but I am leaving out things like magnetic saturation of the core of the iron that I will not get into) Just a side note, if you pull less current than 138ma, the voltage of the secondary will rise slightly. So, unloaded the 660vct might spit out 675 or 680 or some such number, which will in turn increase your DC voltage after rectification. This is one of the reasons you will see transformers with the same secondary voltage but specced for different currents (e.g. 50ma, 100ma 138ma, 180ma), and also one of the reasons solid state amplifiers use voltage regulation (tubes are not so finicky)
2) It depends. The best way would be to ask them. The tech-way would be to keep an eye on the temperature rise of the power transformer as you increase the secondary load.
>> In that scenario, what would happen if we replace the rectifier tube with diodes? The secondary voltage would be higher as tube rectifiers have a much larger voltage drop (there is a chart somewhere) compared to diodes (typically 0.7v drop per solid state diode where for example a 5U4GB will drop 35V at certain loads)
>> By not using the rectifier and its allotted current, would that make more current available on the 6.4 secondary? In absolute terms, absolutely not. The 6.3V winding is a separate winding. In theory, we could argue again about magnetic saturation of the core, BUT, I digress and say the 6.3V secondary was wound for a rated current, and going over that current will cause the temperature of the coil to increase, you will eventually reach the limit of the core and wire. The separate secondaries (660Vct, 6.3V, 5V) do not "share" current in the way you are thinking, but again, some people "cheat" and just pay attention to how much current they are passing based on the size of the wire and the temperature rise of the power transformer. I will state again, this is a good way to possibly burn up a transformer, though. :)
>> Or could the HT deliver a higher voltage or more current to the B+ draws? No, BUT, again, on any secondary, you can always pull more current than specified... the question remains: How long will the power transformer last and will it proverbially catch fire? I know I have had conversations with Hammond (and in fact in some of their literature they used to say "conservatively rated"), and they mentioned they were designed to be cool running, and that you could easily pull more current from any and all secondaries. If you wanted an exact number for the 290BX, why not just call or email them? I bet one of their engineers might email you back and say "yes, you can pull X more current on the 660vct line".