Hmm, I not sure if "piggybacking" will work - I think that the s1mp3 player supports piggybacking due to the way the board is designed. I need to search up more on this to see if piggybacking can be used universally on mem chips.
The "surefire" method, which I believe will work with your player (and mine

), is to solder a new chip into the vacant memory chip solder pad on the board - for most 512mb & below models, only one of the 2 memory solder pads are used (
Here (my player), you can see the unsoldered pad.
Here, on a 1GB model, you can see both pads are populated.
What we can do is buy a mem chip from the link you gave, and solder it into the spare slot, and hope it works. I've checked that the chips his selling are the exact same make & model as the chips in my player, so no worries there. You should crack open your player and check if they're similar -
datasheet for model number.
I'm not too sure if you can have different capacity chips (1GB chip & the original 512MB chip) together. I'm going to get a pair of 1GB chips from him as soon as I get a debit card - see if I can get me a 2GB player! (Really hope that I don't run into the FAT16 Volume size limit...Theoreticall y it is 4GB, but you never know if the implementation by iriver is not complete...)