I got a thought that seemed like a good idea: build an IF-AF amplifier module which is self contained. In that way, I can experiment with new mixer circuits without having to build from scratch every time.
Audio amplifier problems
A search for audio amplifiers brings up a lot of results. I decided to try the circuit shown below. The voltages are what I measured in the finished circuit. However, there was a problem. It seemed OK at first - BUT - loud sounds made the amplifier break into oscillations, making bop - bop - bop sounds. Not good! I don't understand why. The feedback should be negative according to the schematic. But there is obviously something mysterious going on.

The completed circuit
I removed the 820k / 68pF feedback circuit and replaced it with R9 and R10 a bias circuit for Q4. The new complete circuit below:
(EDIT: Corrected typo in naming Q4)

The circuit appears to be very stable. I can touch anywhere without any signs of instability. The output from D1 (to the S-meter) is about 0,5V maximum. Audio signal to the volume potmeter is in the 50- to 100 mV range.
The quiecent current in the output transistors is adjusted with R13 potmeter. I have set it at 1mA. It sounds clean, no fuzzyness on weak sounds. The circuit uses very little current, less than 5mA. It should be ideal for battery power.
A discrete transistor circuit like this has very low internal noise. There is no hiss and battry operation eliminates hum. Thats good!
The circuitboard is 7 cm x 10 cm.

EDIT
A short video: ... touching the IF input
Still to do: Mixer circuit with SA612 ..!
I have not tried using this chip before. I've soldered long leads to to the chip to make it easier to use. It remains to be seen if that is a good idea!
The hunt is on for a good circuit diagram for this chip ..!

Update as of Jan23:
I couldn't get the 10,7MHz IF with crystal filter to work. So - I changed the 1st IF to 2045kHz, using a 2,5 MHz x-tal oscillator. The 2nd IF is at 455kHz. No nice selective filter though ... But it seems to work well.
2nd mixer and 2,5MHz crystal:
Double tuned preselector with inductive copling and 1st mixer, covering 5,5 MHz to 22MHz with BB112 varicaps:
I'm using the arduino VFO. It is really nice and conveniant. However, at a cost. There is some digital noise on some frequencies. I guess I need to move the VFO into it's own shielded box.
My recollection is that a properly operating 602/612 drew about 8 mils or so at 7 ish volts, and when they died, the carcass would still pull a couple of milliamps - they just didn't work ...
This is for just the mixer function and using the transistor as an LO buffer.
73,
Win W5JAG
The Arduino VFO from AD7C works very well ..! It offers several tuning rates, 10Hz, 50Hz, 100Hz, 500Hz, 1kHz, 2,5kHz, 5kHz, 10kHz, 100kHz and 1MHz. Selectable by pressing the tuner knob. I really like it.
So with the new rock stable VFO, I can't resist trying another double conversion superhet. I've given up on the bad SA612 ICs. Instead, I've built a X-tal controlled 10,7MHz to 455kHz mixer, with an old 10,7 MHz X-tal filter. The x-tal filter is a bit wide, with a 15kHz passband. But it is still better than the LC-filter cans at 455kHz, I think.
Now, it is on to building the 1.st mixer!
Bad ICs?
I bought six SA612 off of ebay. I built a mixer / x-tal oscillator circuit as shown on page 4 in the data sheet. However, the circuit appeared completely dead. Curret draw on the Vcc terminal was zero. I tried all six ICs, same result. All of them appeares to be dead.
Am I missing something, or are the ICs actually dead? I find it hard to comprehend that 6 out of 6 components should be defective.
Anyone had similar experiences with e-bay components? I have bought from e-bay before, but this is the first time I am unsure of what's going on.
Today was a good day! I finally found a VFO project that works. It is here: http://www.ad7c.com/2013/11/dss-vfo-update-last-frequency-saved-in-eeprom/
There is still a question about IF offset that I have to figure out in the software code, if I can understand it. When the display reads 10MHz, my scope shows output signal at 5,82MHz.
It is almost like magic. How does 0's and 1's produce clean sine wave: