The "mystery component" is just a packaged diode bridge, probably made from copper oxide rectifiers. The closest available subsitute I can think of would be a bridge made from germanium diodes such as 1N34A.
As for the power supply: no, you can't just add more caps and get rid of the choke. The choke forms an inverted-L lowpass filter along with the filter cap that follows it. Eliminating it would result in much more ripple. Besides, filter chokes are not hard to find; Hammond makes ones that are reasonably priced. The value is right there on the schematic: 15H. The Hammond 158L, at about 17 bucks, looks like a suitable part. It's rated for 75mA and its DC resistance is 400 ohms.
It would be possible to use a resistor (of suitable power rating) instead if you increased the raw B+ by a suitable amount. But for the amount of resistance you would need to get the same effective filtering as given by the choke, it's pretty wasteful of power--power that's spent in heating up the resistor! The regulation would be pretty poor, too, which is an issue when you're feeding a circuit where the current draw goes up and down--such as a tube compressor!
As an illustration, the reactance of a 15H choke at the ripple frequency of 120Hz is 11.3Kohms. You'd have to use a resistor of 11.3K to get the same effectiveness in reducing ripple... and then you need to allow for the whopping voltage drop across that resistor, and the power dissipated by it.
This is why, despite their expense, you almost always see filter chokes used in tube circuits where appreciable current is being drawn.