Look, I understand that this wont persuade you. From other threads, I know you are a hardcore proponent of EMH. But someone else might find this insightful:
Buybacks work in theory, but they depepnd on a lot of factors.
Essentially what you are trying to do is shrink the existing share count, so that EPS goes up which presumably drives your share price up in the longer term.
E.g.:
$10 in net income / 10 shares = $1 EPS. Lets say right now you are trading at a 6x multiple, the market is nervous about your prospects. You think your shares are undervalued and that you are probably worth 10x (perhaps your industry average).
So you buyback 20% of your shares, existing share count decreases from 10 to 8. EPS goes up to $1.25 per share.
But, one of the uncertainties behind a buyback is the fact that you never know when or how much management will actually buyback. They will sometimes announce a plan that would buyback 20% of shares, but only do that over maybe 10 years. Thats why your bit about timing the buyback just doesn't work.
Let's say somehow you do manage to buyback the 20% in just one year (the market hates your company). So with an EPS of $1.25, if the market keeps giving you that 6x multiple, in theory your shares should be worth at least $7.50, not the $6 before. Moreover, if the buyback signals enough confidence in the company, maybe the market will realize it and you will return to the 10x multiple you had before, so your shares go to $12.50
But see nobody can time when the market works or when the market will catch on to the value of your company. Benjamin Graham said that is one of the great mysteries of the stock market when he testified before congress.
It is during that lag time when the share price does not move that investor confidence can waiver and maybe they will sell -- ultimately not realizing the value that eventually comes from the buyback and reduced share count.