you assume that knowledge of one's source code permits a fundamentally more powerful kind of recursive self improvement.

It's not really a difference in kind so much as a radical difference in terms of efficiency.

If asked to improve a C program, do you think a C programmer would rather have a memory dump of the running program or the memory dump and the source code for the program? The source code is a huge help in understanding and improving the program, and this translates into an ability to make improvements at a rate that is orders of magnitude greater with the source code than without. There's no reason to expect the case to be different for programs that are AGIs than for other kinds of programs, and no reason to expect it to be different for programmers that are AGIs than for human programmers. On the contrary, I think the advantage of having and understanding the source code increases as programs get larger and more complex, and is greater for programs that were artificially designed and are modular and highly compressed versus naturally evolved programs that have lots of redundancy and are non-modular.