Can simple DC/DC linear regulators be used in parallel

You said you measured the 1.3 Amps across Vin and GND. This is NOT the way to measure the current capability of a power supply - it does give you the short circuit current, but that is usually not a useful value. If the existing power supply claims to be 12 volt and 900 mA, you should believe that current rating, and not attempt to draw more currrent.

To measure current, you must connect your meter in series with the circuit - you break the circuit to do this.

You should measure the actual current drawn by the 12 volt load. If it is less than 900 mA, then the difference is the current you have available to power your step-down converter.

As others have said, the 300 mA rating of the stepdown converter is the maximum it can supply, not what it will actually draw. Since the stepdown ratio of the converter is 5/12, we can expect the current drawn from the 12 volt supply to be a bit more than 5/12 of the load current - perhaps 35 mA. (As a rough approximation, we can assume that the power into the converter equals the power out, plus some losses in the converter.)

The total current drawn from the 12 volt supply will then be whatever you measure for the scale, plus the 35 mA or so for the step-down converter and 5 volt load.

Aside from the pointless (and possibly harmful) derivation of the pre-regulator reference from the regulated output this is just a Darlington/Zener pre-regulator followed by a three terminal regulator.

By possible harmful- there is insufficient load on the LM317 for low regulator load conditions- there should be at least 5-6mA minimum (typically a 220 or 240 ohm resistor is used where you have 910 ohms) and the Zener current (minus base current) through R1 subtracts from that- you can work it out, somewhere between 0.5 and 1mA reduction. Otherwise the output goes out of regulation- perhaps the reason there's a zener on the output. Without the Zener on the output, the output voltage would rise, causing the input voltage to rise.

It's really wasteful to use a linear regulator like this - a switching regulator would be much more efficient, but if you really need to avoid the switching noise, complementary pre-regulators (zener, resistor, darlington with a protection diode) followed by three-terminal (or other low-voltage) regulators would make as much sense.

Use perhaps a 24V zener and you can get complementary darlingtons in one package with appropriate ratings.

If you are very concerned about noise, there are better choices than the LM317/337. As well as noise, just the 5-6mA Iq results in 0.6W of dissipation before adding any load at all.