Yes, I mean short I2C wires.
No, you don't have to stay away from software I2C. If you are not planning any I2C sensors, and it is only the I2C display, then it can be done with some small changes to the I2C display library.
You have used every pin :confused:
The analog inputs are also digital pins as far as I know. That means you should be able to run a software I2C with any two of the analog pins.
It is possible to use a software PWM library, to dim a led on any pin. That requires a timer with interrupt.
My advice is to make a new board, perhaps with the Micro instead of the Pro Micro.
Second best is the SoftwareWire or the SlowSoftWire on two analog pins for the I2C display.
When you change the I2C display library, you have to be carefull how you organize your files. You should rename the changed library. When the I2C display has an update with bugs removed, you don't get them. You could copy the changed files into your project, so that they will appear on new tabs in the Arduino IDE.
It is possible to use the RX and TX led on the Arduino Pro Micro. When the Serial port is used, they will be overidden, but it is possible to use them. I switch them between INPUT (off) and OUTPUT LOW (on). Their pin numbers are LED_BUILTIN_TX and LED_BUILTIN_RX. The first thing I do is to turn them off, because they are so bright.
The design of the Pro Micro has a flaw. When you have soldered the T1 for 5V, and connect the power to RAW and connect the USB to a computer, then it is possible that current can flow into the computer.