As someone who has dealt with gift aid for a charity, just a reassurance that the charity dies not know anything about your financial affairs apart from that say you've made a £20 donation, that you have paid £20 in tax. The other thing is that it reduces the amount of tax you pay that year.
If you do your return and pre gift aid you are due to pay £40, but you have made a donation, you only are due to pay £20 tax ( so it is a way to make a further donation to the charity) if you donated £40 over the year, no tax due, legally.
As well as being extra funds to the charity, gift aid income is unrestricted funds. So much charity income in the form of grants has to be spent on a particular thing, quite rightly, if you get a grant to do a particular project, you have to spend it on that. Unrestricted funds can be used for other things, such as running costs, or projects that are not as attractive to grant funders
If you can gift aid something, a donation, or whatever then do gift Aid
Don't get too hung up on how much a shop raises on your donation, it might have been v dear, and you lived it, but things are only worth what people are willing to pay. It's better than putting it in landfill isn't it
If you think you can do better with selling the stuff, just sell the stuff, and donate the money (and gift aid the donation!)