I have been using an ancient Korg DT-1 that was about $125 when I got it. I would happily pay the same for another like it; but, of course, they discontinued that model about a week after (or maybe a month before) I got mine.

It has selectable "slow" or "instant" settings on the mode switch, and in the "instant" mode, it can be pretty erratic - so I just "always" use the "slow" mode.

The CA-30 is a "near the bottom of the barrel" tuner, meant for low price, portability and "good enough" tuning for the typical session musician. It probably has a relatively short "sample interval" setting that is likely a little slower than the "instant" option on the DT-1, but not as long as the DT-1 slow mode.

Both the built in microphone and the contact pickups likely use piezo-ceramic elements - probably barium titanate or the ever-popular PZT, which are essentially small capacitors that "generate" a charge proportional to applied pressure - or in the case of the pickup, to applied acceleration.

The dimensions chosen for the piezo element can have a significant effect on the output. A larger diameter may produce more "charge" but also has a higher capacitance. A thinner element usually is more sensitive to the applied pressure/acceleration - but again the higher output may be swamped in the increased C. While a sophisticated design would require consideration of many different compromises, the usual procedure in instruments of this kind is to pick a convenient (cheap) size and "adjust" in the circuitry.

The new Korg pickup is more likely to have a charge/capacitance balance similar to what's in the Korg microphone (although there's no real guarantee of that, obviously the "time constants" when you use the Korg pickup are working better for you than when you used the Matrix pickup.) I'd suspect that the Korg pickup has a somewhat larger cross-section, and maybe thinner, "element," based on the response you've seen.

I haven't found a reference to a model number for your Seiko tuner; but it's rather academic, since Seiko apparently doesn't consider tuners to be a sufficiently significant "product line" to even acknowledtge them on any of their (several) product information web sites. If it's not a "better than average" product, repair is probably not really worthwhile. As I'm sure you're aware, unsoldering is a lot more difficult - and more likely to damage components - than soldering, so if you have to pull the display out to get to the connector, you're into risky territory.

There are "electrical cold solders" available, basically paint or epoxy with a lot of silver or other metal in them to make them conductive. Unfortunately they're not widely available, and it's even more difficult (unless you're a large volume industrial user) to get any useful specs on them. Since the piezo (microphone/pickup) part of the circuit is inherently very high impedance, a "resistive" connection is about as good as a gold-plated one, so you might be able to "paint" a connection if you can find a suitable material. Of course, after you get an electrical joint, you'd likely still need something additional to make it a solid mechanical joint.

It sounds as though the Korg pickup has solved the immediate problem. Good news is always nice to hear.

John