We're going to dynamically add a ground to each "column" of sensors; the idea being that we can attach multiple oscillators to the same input pins, and activate only the column we want to read by giving a ground to the "left-hand-side" of the circuit. Instead of connecting and removing the blue wire, we're going to set an i/o pin to a high output, then turn it to an input. By turning the pin to a (high impedence) input pin, we're effectively removing the power source and setting the oscillator running.
Now we need to create a grid of sensors, attaching multiple oscillators to each i/o pin. Consider the diagram below (we're still not sure this will actually work, but this is the theory so far!)
Note the resistors on the i/o pins. Although the PIC has internal clamp diodes to enable it to cope with reversed voltage (from the inductors during oscillation) we need to have high value input resistors to protect the internal clamp diodes from too much current.
Let's say we want to read the left-most column of sensors. We set the output pins on the shift register such that Q0 is low and Q1-Q7 are high. This means that the capacitors and inductors C1-C4 and L1-L4 have no ground connection and - in theory - are taken out of the "read" part of the circuit.
If we turn PORTB into an output and make the entire PORTB high, capacitors C5-C8 should begin to charge and only coils L5-L8 have a ground connected to them (capacitors C1-C4 and coils L1-L4 have no ground connection and should not be affected). Now let's concentrate on just C5/L5:
If we make all of PORTB an input, C5 should begin to discharge. But there's nothing stopping it discharging through coils L6-L8 as well as (or instead of?) L5. But if we make ONLY PORTB.0 an input, C5 should only be able to discharge through L5 (since L6-L8 has power still connected to the "right-hand" side of the circuit). So we should be able to read the time taken for the current to oscillate through L5 and use this to determine whether or not a metallic object is interrupting the magnetic field of L5.
We then turn PORTB.0 to a high output pin and turn PORTB.1 to an input pin and repeat for L6. After reading L6, we should be able to read L7 and L8 in a similar fashion.
Now presuming all this actually works, we should be able to adjust the output from our shift register, to make Q0 high and send Q1 low (keeping Q2-Q8 high). This in turn provides a ground connection for the right-most "column" of sensors only. By repeating the reading process, we should be able to detect the presence of metal objects above L1-L4.
At this stage, it's all supposition and makes a lot of assumptions. But there's only one way to find out if this will actually work - and that's to make up a PCB and give it a try!