I don't know the 555 timers - I have always tried to avoid them because of problems like these.
All I can suggest is that you simplify your circuit with a D type flip flop (4013) configured with the Q o/p wired back to the data input. A low going edge at the clock input driven from your touch...
Just to say that the transformer isolated 3phase route is the only one to take - however it's worth mentioning that 240VDC is extremely dangerous and you must take extra safety precautions when handling and using the supply. Anyone using the boat must be told about the hazard. If you get hold...
Let's try to clarify what you want. The old chip produced 2 outputs for a processor, 1x the input value and 2x the input value. You now need a circuit which will simulate that action and it needs to be simple.
Could you use a simple analogue switch like the dirt cheap CMOS 4066 operated by...
I am not going to disagree with any of the above all of which is good information from engineers clearly more experienced with synchros and resovers than me - last used when I was a much younger man.
If at one time this system did work no matter how poor the resolution, your task is to get it...
You need to describe this in terms of current and then we will be able to understand what you need. Measuring resistance (reading in) is done effectively by applying a known voltage and measuring the current or comparing resistors in a bridge circuit.
Outputing resistance as you put it is...