What is the best delay to use between characters sent to the serial port
SoftwareSerial has a considerable overhead. It can often send at 115200 successfully but 9600 is about its limit for receiving, and you're trying both send and receive. In addition, for each character your code receives, it transmits considerably more than that 1 character (11 characters, by my count). It isn't too surprising that it would fall behind. You will need to either reduce the size of what you echo or reduce the rate at which you send characters to it (which is what you accomplished with your delay) so that the transmission (echo) rate can keep up.

Update:

The OP reports success with continuous reception by, and transmission from, the Arduino at 57600 baud (but not at the same time). The transmission rate would be consistent with my experience transmitting at 115200 baud (blindly and for short bursts, to reconfigure ESP8266-01s that were shipped with a preset 115200 rate.