The regulator is beginning to drop out. You really need a minimum of 6 volts for it to regulate properly...this explains why you are not seeing 250ma's.
The formulas are 1.25/ohms = current.
1.25/current = ohms.
1.25 is the reference voltage the regulator uses and you should always see that voltage between the output and adjust pins of the regulator.
Don't use those little square 9 volt batteries as they will not power it for long and are not made to deliver high currents.
If it was me I would get a 6 AA or AAA battery holder. You could use Alkaline or Nimh batteries and it would a no muss no fuss solution. Or you could use a pair of AA li-ion batteries.
At 5.3 volts, I the regulator will be out of regulation with the GB diode hooked up. I know this isn't what people want to hear but others have had problems even using a pair of CR123's. The voltage sags to the point the regulator begins to drop out.
Because you are not putting enough of a load on it. A silicon diode has about a .7 volt voltage drop. You need 4 silicon diodes hooked in series to simulate appx. what a GB diode will pull.