My answer is different and tells you exactly where you stand.
Take a look here for the share identification rules. You are certainly not being hit twice.
The fact that your broker allows you to buy and sell shares within a 20 day period with no cash outlay is irrelevant as far as the tax rules are concerned. If you "buy" some shares in Company A and "sell" them 20 days later, the purchase will have been added to the the Section 104 pool of shares you already have in Company A and the gain or loss on disposal of those shares will be based on the averaged cost of those shares in the Section 104 pool.
I hope this clarifies matters for you. I'm sorry the news isn't better but the rules have been written to stop the shielding of gains by so called "bed and breakfasting".
Let me know if you have any further questions. If you want me to answer any follow up questions you may have, you will need to mention my name, Tony, in your response.