Here's a neat trick how you can avoid renaming the srm files in AST. 
It works on snes9x and should also work in sd2snes, but not zsnes/higan/bsnes. 
The trick uses the feature of snes9x to make a shared folder with the sram files.

- have snes9x (latest version 1.55: https://dl.qwertymodo.com/snes9x_msu.zip )
- make 4 new folders in your emulator section (e.g. AST1, AST2, AST3, AST4)
- copy the 4 weeks' roms into their specific folder
- RENAME each rom in the 4 folders into the same name, (e.g. all roms are called ast.smc: rename AST1/bszelda_ast1.smc -> AST1/ast.smc, AST2/bszelda_ast2.smc -> AST2/ast.smc...)
- load your desired week's rom from the specific folder. No matter which week you load, it always uses the shared srm!

So, you will also be caused to rename the files, but this time only the roms. Since snes9x will use the same srm for all roms then 
(since all have the same name), located in the "saves" folder, no further renaming of the srm is necessary :)
After finishing week1: AST1/ast.smc, just load AST2/ast.smc to carry on your progress.

snes9x 1.55 and sd2snes also support msu1, but in this case you will need to rename also all the week's specific pcm:s and the msu file into the same name, 
like bszelda_ast1.msu -> ast.msu, bszelda_ast1-1.pcm -> ast-1.pcm, bszelda_ast1-2.pcm -> ast-2.pcm and so on for each week. 
Since the week specific msu1 files are located in the specific week's folder this should work without problems as well.

So one correct setup required and you can have fun without bothering renaming the stuff ever again...!