1), the wiring diagram might not be literal. You should be able to determine by testing the switch what pins are what.
2), you can replace the caps with any ceramic cap, and it will probably work perfectly fine. Even with no cap, it will probably still work fine.
3), why are you replacing them? Are they shorted, or are you just trying it to see? If you test them for short (in circuit), and one shows short circuit, keep in mind that the switch will always be in one of two positions which looks like a dead short, so make sure to throw the switch if one cap tests short to confirm. If you test them and meter shows (counts to) infinity, then changing them won't make a bit of difference in your problems.
4), if you have a DMM with an amp function, you can put your meter in series with motor and power it up with the appropriate voltage, preferably (but not required since you have a DMM) with a bench power supply that has a current meter. See how much current it is drawing. Use that to figure out how many watts it is consuming. If it is drawing 1 watt, your 1/2 watt resistor may not long for this world.
5), did you already test C270 for short? It's far more likely to go bad than the ceramic caps.
Fusible resistors are not like actual fuses -- they take awhile to burn up, not instant, even if spec is exceeded. The mechanism function shift motor only runs one cycle for each change of deck function. This cycle is like less than 1-second, not continuous. And then it stops. Is it possible that the servo mechanism is not working properly causing that motor to run continuously? Or are the caps shorted causing excessive current draw?