Before anybody closes this... I am not referring to the current method of obtaining skins.

How do I change the old skin? (Obtained through Method 1)

I know the upload box in your Minecraft Profile page changes the result for the new (second) result, but is there any way to sync or at least change the old (first) method?

As you can see, the skins on both URLs (for the same user) are different. (not in the sense that one is the newer 64x64 format and the other is still 64x32 but they are both completely different skins)
One is some sort of futuristic armor guy in a dwarven armor, while another is a... Er.. this.

Link 1: http://s3.amazonaws.com/MinecraftSkins/aytimothy.png
Link 2: http://textures.minecraft.net/texture/46e54b38ca489583f5f3e69cd0f25c50adcf29253fc5169dc6abafdc4770

Can I change the old skin (obtained through the first method) with baked textures (anything on the armor layers goes onto the actual skin layer) so that it'll appear the same in pre-r1.3 versions?

In Minecraft, there are currently two ways of obtaining skins.
The following examples are with my own skin.

The old Method:

1. Find the username's skin through the Amazon CDN links or via the game site.

   GET http://s3.amazonaws.com/MinecraftSkins/aytimothy.png
   

   or:

   GET http://skins.minecraft.net/MinecraftSkins/aytimothy.png
   

And that's it. (Literally)
Note: The skins.minecraft.net link has been updated to retrieve the skin from textures.minecraft.net (second link).

The new Method:

1. Find the username's UUID from the Mojang API.

   POST https://api.mojang.com/users/profiles/minecraft/aytimothy
   

   Which results in something like this:

   {
    "id": "29c91bd0538b4fb6b212e2393faff119",
    "name": "aytimothy"
   }
   

2. Find the Base64 string that contains the skin/cape texture link.

   GET https://sessionserver.mojang.com/session/minecraft/profile/29c91bd0538b4fb6b212e2393faff119
   

   Which results in something like this:

   {
    "id": "29c91bd0538b4fb6b212e2393faff119",
    "name": "aytimothy",
    "properties":[
        {
        "name": "textures",
        "value": "eyJ0aW1lc3RhbXAiOjE0MzM1ODA2NTQwNDUsInByb2ZpbGVJZCI6IjI5YzkxYmQwNTM4YjRmYjZiMjEyZTIzOTNmYWZmMTE5IiwicHJvZmlsZU5hbWUiOiJheXRpbW90aHkiLCJ0ZXh0dXJlcyI6eyJTS0lOIjp7InVybCI6Imh0dHA6Ly90ZXh0dXJlcy5taW5lY3JhZnQubmV0L3RleHR1cmUvNDZlNTRiMzhjYTQ4OTU4M2Y1ZjNlNjljZDBmMjVjNTBhZGNmMjkyNTNmYzUxNjlkYzZhYmFmZGM0NzcwIn19fQ=="
        }]
   }
   

3. Decode the Base64 compressed string...

    eyJ0aW1lc3RhbXAiOjE0MzM1ODAxNzg4MzUsInByb2ZpbGVJZCI6IjI5YzkxYmQwNTM4YjRmYjZiMjEyZTIzOTNmYWZmMTE5IiwicHJvZmlsZU5hbWUiOiJheXRpbW90aHkiLCJ0ZXh0dXJlcyI6eyJTS0lOIjp7InVybCI6Imh0dHA6Ly90ZXh0dXJlcy5taW5lY3JhZnQubmV0L3RleHR1cmUvNDZlNTRiMzhjYTQ4OTU4M2Y1ZjNlNjljZDBmMjVjNTBhZGNmMjkyNTNmYzUxNjlkYzZhYmFmZGM0NzcwIn19fQ==
   

   Which means:

   {"timestamp":1433580178835,"profileId":"29c91bd0538b4fb6b212e2393faff119","profileName":"aytimothy","textures":{"SKIN":{"url":"http://textures.minecraft.net/texture/46e54b38ca489583f5f3e69cd0f25c50adcf29253fc5169dc6abafdc4770"}}}
   

This results in a final URL of http://textures.minecraft.net/texture/46e54b38ca489583f5f3e69cd0f25c50adcf29253fc5169dc6abafdc4770