Before you make the commitment of the Canon 100-400 (I think you refer to the Mk1 in your price range), take a look at the review for the performance at the top end of the range.
It is known that there was a fade to softness at the 400 end and a tendency to attract dust due to the sliding function in changing range - not for nothing was it known as 'The dust-pump'.
Notwithstanding, it remained/remains a hugely capable optic, but is now far surpassed by the Mk2 version.
As I say, it's still a tremendous optic.
I do miss my time in the RAF, but every month it reminds me how great it was with a lovely big cheque
...Bigamy is having one wife too many, - Monogomy is much the same...(Oscar Wilde)