as far as i understood you, those 300mm arent enough
well you gave already yourself the answer ;)
400mm and a double (2x) extender, giving you 800mm, the extender might work even with your 70-300 which would be 140-600 on your actual zoom lense
but keep in mind that extenders "eat" aperture, meaning the lense wont be that fast enough, with that in mind you are left with only a few fast choices from canon, if money is not an issue (with rentals) , go with the 400 2.8
500 4 and 600 4 are also options, with or without extender
and dont forget your sturdy tripod / monopod
my advice would be to test your actual lense and your choosen rent lense in the shop for compatibility with the extender, and also to find out which lenght suits you best