Advanced to 113 bytes:

Code:
<input onkeyup="s?e=Date.now():s=Date.now()"onblur="c=this.value.length;this.value+=c/(e-s)"><script>s=0</script>
If I coudn't go without global script there're two other options. Tried this, not working:

☑ c=this.value.length;this.value+=c/(e-s)
Ø x=this.value;c=x.length;x+=c/(e-s)

And if there's no way of shortening segment too:

Code:
onkeyup="s?e=Date.now():s=Date.now()"
the upper [+ span of 20 symbols maximum] (on the cost of <scripts> elimination)

I'll put my hands carefully up.