Is there a gear ratio that would allow you to get the power and speed of a 393 motor out of a 269 motor?
A 393 in default mode is the same speed as a 269.
If a 393 is in high speed mode a 269 at a gear ratio of 5:3 will be really really close.
Remember you will never have the power of a 393 because it is just a bigger better motor.
You can’t have both the torque and speed of a 393 but you can have one or the other.
Like others have already said, gear ratios don’t magically increase the speed and power of your motor. Energy can be neither created nor destroyed, only transformed into different forms. 393 motors are inherently stronger than 269 motors and while you can get the 269 to have the same speed or the same torque as the 393 motor, you cannot have both.
The relevant answer here to your question, though, would be that if you put the 393 in the same place the 269 was with no gearing changes, it will be the same speed but with more power behind it, which will help solve stalling issues.
From your post it seems like you’re trying to salvage as much power as possible to fuel your robot. As I’ve be taught, there are no limits to air or rubber bands, so why not use it to your advantage?
all the motors spin at the same RPM except for the 393 in high speed mode which spins at 160 RPM. you wont get the power of a 393 out of a 269 without compromising speed.