That difference seems to arise because the report you cite uses a broad definition of influenza deaths. Page 2 says they're counting patients who "have influenza as a contributing or underlying cause of death, plus patients who received specialist care with an influenza diagnosis who subsequently died within 30 days".
In any case, boosting the number to 685 still isn't enough so that covid is "double at most", and boosting it to 1100 isn't enough either.
As far as I know they have an even broader definition of corona deaths in Sweden.
My point is more that statistics is hard. You tried to debunk someones "dodgy" statistics with your own numbers that can be twisted to be even more off than the person you tried dismiss.
I'm afraid nobody and everybody will be right after this is over. People will always find statistics to prove their points and that they where right and the other people where wrong.
In any case, boosting the number to 685 still isn't enough so that covid is "double at most", and boosting it to 1100 isn't enough either.