You can convert those GIFs into WEBMs using Gfycat...a 20MB GIF will probably end up being like a 3-4 MB WEBM and it will upload faster. Keep in mind when you post WEBMs you're going to want to go to "upload WEBM" instead of the normal upload page.
At any rate the captcha only affects new users...I forget how long it lasts on a new account, perhaps a week, anyways it will go away in time and then it won't matter how fast you upload. Considering you joined about 4 days ago it should only last another 3 days.