OK, so building on all the excellent tips from the guys above, I have done a few hours of testing. I tried a load of different combinations, and I have found one that seems to work.
So in summary I have managed to get Webfonts to work on Chrome with WebGL and with the pop-in suitably hidden. It seems to work perfectly for me, I have tested with 3 different textbox objects and 5 different instances of each, all on screen at once. I would appreciate some others testing this same method, to see if it's just working on my machine/setup etc.
I would also like to reiterate that this is all stuff already suggested by Paradox, Dave Hailwood, Thndr etc. But I just wanted to share that I put it all together and got it to work how I wanted, maybe it might help somebody else as fussy as me:
Textbox1 [On Created]:
> Textbox1: Set Invisible
> Textbox1: Set Font Size to 0
> Textbox1: Set Web Font 'Font_Name' from 'Stylesheet.css'
> System: Wait 0.6 Seconds
> Textbox1: Set Web Font 'Font_Name' from 'Stylesheet.css'
> Textbox1: Set Visible
> System: Wait 0.6 Seconds
> Textbox1: Set Font Size to 12
(Be sure to use 'On Created', as this is called before 'Start of Layout'. This is all tested with local embedded Webfonts too.)