Since the original oscillator of 5.0688 can not be speed up, we need to reduce the divider stages.

Calculations

For 9600 baud, the original divider scales down the clock by 5068800 / (16*9600) = 1:33.

To reach 38400, we divide by 8 and get 5068800 / 8 = 633600. 633600 is fed into the UART and gives 39600 baud . This is just 3% faster than 38400 and well acceptable.

Changes to the circuit

To get a divider by 8, we bypass the 1:12 divider E12 and disable the feedback XOR gate in E29.1/2/3.

schematic modified small

 

Step by step

Reworking the board is easy, you need parts for less than $1. Only IC E29 is touched.

patched 7486

  1. Remove the existing E29 7486 and replace it with a DIL14 socket.
  2. Get a new 74LS86.
  3. Bend out pins 13, 1, and 2.
  4. Connect pin 12 to pin 1 with a wire. Pin 2 is left open and internally pulled to H.
    (On the picture I connected pin 12 with pin 2 instead ... it doesn't matter.)
  5. Plug the manipulated 7486 back into socket E29.

patched dl11-w

Sínce all changes are made only to the 7486 chip, you can restore the DL11-W to its original state by plugging a regular 7486 into E29 socket again. Good to know!

New baudrates

Now on E27 we have:
Pin 14(Clk0) = fIn = 5068800
Pin 9 (labeled "9600 baud") : fIn/4 = 1267200 = 79200 baud (unusual)
Pin 8 (labeled"4800 baud") : fIn/8 = 633600. = 633600 / 16 => 39600 baud = 38400
Pin 11 (labeled"2400 baud") : fIn/16 -> => 19200

The divider E28 is left unchanged, so  "1200" becomes 9600, "600" becomes 4800, "300" becomes 2400 and "150"becomes 1200.

The circuit for the 110 baud (E39,E26,E19) is also left unchanged, so 110 baud are still available.

If the original 5.068800 Quartz is used, baudrates are not accurate. Remember that 1:33 divider for 9600 baud? Now we generate 9600 with an 1:32 divider. So all baudrates are 3% over regular speed., this is considered to be tolerable.

If you want exact timing for 1200..38400 baud, you must replace the original 5.068800 MHz oscillator with a 4.915200 MHz type. But then the 110 baud has 3% under speed.
Better use a 5.000000 MHz oscillator, then there's a 1.5% speed error on all baud rates. Luckily there are so many alternatives!