Electronic – increasing metal detector range

I am working on my senior project. As part of my project I need to use a metal detector. I am using the following circuit schematic.

The principle is based on the properties of inductor coil:

$$L=N^2\mu \left(\frac{A}{l}\right)$$

Where \$N\$ is number of turns, \$\mu\$ magnetic permeability, \$A\$ is area of the coil, and \$l\$ is the length of the coil (if you think of coil as cylinder, l is its height).

Once a metal object is placed near the coil, it behaves as a core for the inductor, and the \$L\$ changes, it becomes:

$$L = L_{air}\times\mu$$

Hence RLC circuit frequency and the following sound produced by the speaker changes as well. When I set up the circuit, I have used a small inductor about \$1\space\mathrm{cm}\$ in size which was \$10\space\mathrm{mH}\$, as it was specified in circuit (there are different variations of the same circuit with small differences), it was detecting the metal, but the range was very small, at most \$1\space\mathrm{cm}\$.

I researched how I can improve the range (not in academic articles, because I could not find anything specific, would be happy to hear suggestions from you) and read that area of the coil is very important, so I calculated and came up with \$100\space\mathrm{m}\$, \$150\space\mathrm{turns}\$, \$10\space\mathrm{cm}\$ in radius, and \$2\space\mathrm{cm}\$ in length coil.

I bought the wire, and wanted some appropriate round shaped object for that. I went to a place which cuts figures from acrylic, and got this:

Now when I connect it to the circuit, sensitivity is even less. I can't get the reason, possibly because of the magnetic properties of acrylic, I tried to look in internet, but the datasheet provides just the electric properties.

Now I am stuck, I have heard that people got \$40\space\mathrm{cm}\$ range, which is more than ok for me. I don't have time to build a different detector. My questions are:

1. Should I remove acrylic layer?
2. How can I increase the range? (I have different resistors and capacitors, and a potentiometer, which I can use, but I doubt that they will help with sensitivity, any offers for increasing range are ok)
3. I am using 9V batteries and they discharge very fast, how do you think what might stand behind it? Sometimes I use potentiometer instead of resistor, and try all values. May it be due to very low resistance?