Super cool routine!
Okay, with the help of Will_W and Player_, I got this routine:
Program Write-Back
Call this first (I mean first, have it as the first line):
Asm(21788411DF83010900EDB0

then, this:
Asm(21DF83E7EFF1421A47131A4F13131321959DEDB0

Attached is the source code that makes it work.  Please note that you cannot corrupt the last 9 bytes of tempSwapArea (L4).

NOTE: This routine is buggy and obsolete.  Please look ahead for a more appropriate solution.

*EDIT*
Added a .gif of it in action

Well, the first routine gets the name of the program from OP1 and stores it to the last 9 bytes of tempSwapArea.  The last routine restores the name to OP1 and looks up the program, finds the length, and copies the program from 9D95 back into the original location (writeback).  That means you can modify any data that came from a [] statement and it will get saved back.  I'm not too sure though, because when I was playing around with it, I found that it crashed under certain conditions, such as If statements, While, Repeat, getkey().  I think Axe may use the last 9 bytes of tempSwapArea, which would explain it.  I'll look into it in a minute here and see if I can fix it.

*EDIT*
After comparing WikiTI's documentation of tempSwapArea to Axe's documentation of tempSwapArea, I found that tempSwapArea is 323 bytes long, but Axe only gives you 232.  I'll try revising my code to store to a different location and see if it works a bit better.

That's exactly what it does, but I can't figure out why it crashes when you use certain tokens in your Axe program.  Anyone care to look at my source code and try to figure it out?

I've been trying with Wabbit.  Look back a few posts to find the code.

Repeat getkey(15)
EndDissassemles to:
Start:
 ld hl, $FD40
 call Label1
 jr Label2
Label1:
 ld a, h
 out ($01), a
 ld h, $00
 in a, ($01)
 and l
 ld l, h
 ret nz
 inc l
 ret
Label2:
 ld a, h
 or l
 jp nz, Label3
 jp Start
Label3:
 ret

Actually, looking at your hex codes, it seems like you are mixing up B and C when loading the size of the program. It is stored as little-endian. Also, since you are skipping the BB,6D bytes you may want to decrease BC twice to make sure there is not an overflow.

Great, it worked!  Here are the new routines:
Program Write-back
This routine will allow you to save any changes you make during your program to data stored with the [] tokens.  Run this code in the very first line
Asm(217884118483010900EDB0

And run this to save your program:
Asm(218483E7EFF1421A4F131A4713131321959D0B0BEDB0

This routine uses the last nine bytes of L4 (tempSwapArea), so be careful not to modify them.

Attached is the code/hex.