Hi! First, congratulations on your GST!
I was a huge a GST collector before it got discontinued. The bag was super popular and you had to get on wait lists when the seasonal colors came out.
I 100% agree with
@880 the GST is a classic and the rationale for it being discontinued was the low price point. My SA at the time who was connected with Chanel HQ, said that Chanel knew it was priced too low, but there was no way they could make a huge price jump. Hence, GST just got discontinued. You can see similar tote styles now at $5K, but none compare to the functionality of the GST in my opinion, and I have looked at every new tote that has come out since (I'm a tote gal).
That said... moving on to your concern...
I have 6 GSTs, and all of them have the worn bottom corners. I do not baby my bags, and I used them very rough (e.g. stuffed them under airplane seats). It's a great bag and very tough! My bags also slouch.
My suggestion is to leave it and do not refurbish it. Why?
I had two GSTs that were getting floppy, my white and pale pink. Back then, I was getting annoyed at the slouch, so I had them refurbished at Leather Surgeons. The bags came out looking brand new, very stiff and they stood up straight.
But... they were too straight, super stiff, and both lost the beauty of soft leather. What Leather Surgeons did was to add stiff sides to reinforce it. They told me that up front, so I knew. I thought it would look like the original, but no... it looked a bit cheap to me.
Worse... the original "shine" of the GST leather was completely lost. It was now more of a satin/matte. I contacted them, and they said they could shine it up more. I sent it back (the white one), and even after the second attempt, it was never the same shine as the original. The slickness of the original polished leather was also not the same; it felt a bit more "natural" unpolished.
Note though, this is very subtle, and some people may not even see it. My husband did not notice it, and I had to show him and make him feel the difference which he then saw. I tend to be a detailed person, and I see everything, hence I noticed it immediately, especially since I also have 6 GSTs to compare.
Since refurbishing those two bags, I rarely wear them as they do not feel "original" to me. My white GST was my favorite as I love white bags, so it's really a shame that bag lost its leather beauty. If the GST ever comes out again and in white (zero odds), I'm going to buy a new one! The good new is I have other white bags now I can use (if you like white bags with big space, look at the new Bowling Bag from 23P... I bought the small size and love it).
I have said to myself I will never refurbish a bag, not matter how beat up it gets. It's part of my bag's journey with me, through all the experiences of life (e.g. airplanes, restaurants, yup... you name it)!
As for a GST slouching, I spent so much time analyzing why it slouches.


It no longer bothers me, and on the contrary, I find that look rather charming, the sign of a well-loved bag.
Here is why I think it slouches...
I use the back inner zipper pocket to hold my lipsticks. I'm lipstick person, so I usually have 3 lipsticks in that pocket in addition to keys (at the time when I used keys for my car). That back inner zipper pocket gets heavy, and that is what causes the slouch.
You can do a test... put your fist in the back inner zipper pocket and push it down. You can see the pressure of the areas where it normally slouches. Then, put your fist in the open larger compartments. Nothing... no slouch. It's overstuffing the inner back zipper pocket that causes it. Even then, I don't care and still load it up with my lipsticks!


All my GSTs have that cute little slouch.
My two cents...
Keep your bag and use it as is. It's a gorgeous bag, and if it gets beat up, you will look carefree chic which is how I prefer to look when wearing luxury goods. I don't like the "my bag is precious" look. Totes are coming back now... logos are still full force... perfect for the GST.
That's just my thoughts to share. I hope this helps, and congratulations on your gorgeous GST!