Hmm not sure it would be, do you find the 400mm end not reaching far enough or is the lens not fast enough i.e f/2.8 for example?
Your L lens versus the the sigma is nearly similar in F stops given the extra 200mm and the f/6.3 vs 400mm at f/5.6.
I have had for over 8 years now the Sigma 120-300mm f/2.8 EX APO DG HSM (note non OS) with a Canon 2x mkII.
This gives 600mm f/5.6 which is a little quicker than the f/6.3. And a lot quicker without the 2x from (120) 150-300mm of course.
The f/5.0 at 150mm is quite slow compared to the f/2.8 up to 300mm.
I have looked at the specs for its weather resistance & it does look impressive there though.
So just my 2 pennies worth that Sigma do an OS version of the 120-300mm F/2.8 now, pretty costly of course.
But the older non OS I have can be had for £500+, I've seen one on eBay this week still there as of today.
So maybe if the extreme weather ability isn't what you need, mine has survived a down pour on occasion, the extra speed even with a 2x might be an option.
Here's a few examples of my Sigma 120-300mm f/2.8
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