To run the new ruleset, you'll need to recompile Golly, with a replacement for one of the files:
Then you can open this file, and set it replicating:
I'll add some more explanation for what the modifications were and why I thought it was worth bothering. For the moment, open the RLE file above to read about the modifications.
Here are some images of the self-replicating machines in action:
1) Near the beginning, the tape is flowing out in two directions, constructing two machines at the same time. One machine is rotated by 90 degrees, using the rotational-invariance properties of the modified CA. Unlike von Neumann's design, our self-replicators don't need a machine body to start constructing since the tape has this ability on its own.
2) A little later, each of the two original copies has finished copying the tape, and they are constructing the next generation. For a while growth is thus exponential but soon the new copies collide with the old tapes and growth slows down.
3) Here's the body of the machine that the tape makes for itself. On the left is a large block that just recognizes the tape mark: 11111. When the mark is seen, a pulse passes through a 3-counter, and various switches toggle a 6-period pulser on and off, sending 'extend forwards' signals down to the output on the right. Basically the machine extends its ouput line in a loop of the right size (based on the tape that is controlling it) before directing the tape down that line and shutting down. When the tape has filled its new container it flows out through the splitter in two directions, causing two new children to be constructed.
I can explain the details if you want, but it is more fun to design your own machines.
This design owes a great debt of gratitude to Renato Nobili and his WJVN help pages:  which explain how to make different controlling and logic organs in von Neumann's CA. And the design wouldn't have been possible without the Golly support for JVN rules, to try things out. Thanks!