"Now the problem I'm having is the antenna. I've settled on a 1m long aluminium broomstick. Drilled a hole on one side, and with a screw attached a 10 cm copper wire with connector which connects to the antenna pin. The moment I connect this the frequency of the oscillator drops to about 870 kHz and becomes rather unstable, with a variation of +/- 3 kHz, me not moving." - wvmarle
The drop in frequency is expected, it's due to the addition of intrinsic C of the antenna to the tank. And the antenna will pick up all kinds of hum, noise, air currents, small movements, etc.
[EDIT] If you aren't already, I highly recommend you power the oscillator with its own 3 terminal voltage regulator. A lot of frequency instability and drift can be removed that way.
"A piece of wire, about half a meter long, drops the frequency to 988 kHz. Changing my distance from 20 to 40 cm gives a 1-2 kHz response. Looks really good. Unfortunately my work room is too small to make bigger movements (yes, it's tiny). Overall not as rock stable though as no antenna, I guess electrical equipment like my monitor and CFL desk light are too noisy."
It will never be as stable as no antenna.
"Is this pipe simply too big an antenna? My inductor possibly not good enough? Any other suggestions?"
Put a 1pF cap in series with the 10:1 scope probe and measure the voltage swing at the antenna, taking into account the capacitive divider formed by the 1pF and the probe C. It should be a sine wave, and the voltage swing needs to be some tens of volts in order to overcome environmental interference and give you a larger field.
Also with your scope, you can examine the main source of the noise by doing an FFT, or by setting the trigger delay to a multiple of the mains frequency period and look for islands of stability. It's usually mains hum that's the biggest interferer, and you might be able to minimize this by sampling at some integer multiple of the mains frequency, and/or by filtering it afterward in software.