I don't think this is a browser bug, but rather a bug in the upload program. I tested with uploading a 1GB and 2GB file and the upload started right away without waiting at all.
Make sure your test is valid but I found the following unexpected behavior.
case 1:
1. begin upload 1G file
2. upload started normally and progress is normal
3. before completing upload, click on Browse and upload a 2G file
4. upload started normally and progress is messed up. showing negative speed and stuff.
case 2:
1. begin upload 2G file
2. upload started normally and progress is normal
3. before completing upload, click on Browse and upload a 1G file
4. upload started normally and progress is messed up. showing negative speed and stuff.
case 3:
1. begin upload a 1G file
2. upload started normally and progress is normal.
3. start a new tab and begin upload a 2G file
4. upload started normally and progress is normal.
looks like your program is not handling the first two test cases, it doesn't look like a browser bug.
before disabling the upload button once file begins, try to find out why "cancel" upload is not working (if you have implemented it). it looks like there are some success to cancel file upload wtih html5 on client side.