Flaxton - if you use the KED or the traction splint inappropriately you don't put the crew at increased risk nor do you endanger the life of the patient so your analogy is invalid. As it happens ours get used quite a lot.
My remark about saving the paramedic a walk was intentionally flippant but you haven't answered the question about showing a need for the winch before spending the money on it. Yes the trustees can use the donations as they wish (we've been round this buoy before) but what will you do if the winching goes wrong and the public stop donating? Your remark about the public having a right not to donate is rather arrogant - have you asked them all if they want to pay for the extra capability?
You are also changing your tune since you stated previously that the winch would only be used to deploy the paramedic, now you talk about repositioning the casualty as well - this is the sort of mission creep that turns into full blown rescue attempts.
And you want to do the fell/mountain rescuers jobs for them as well - if the casualty is in an inaccessible place then call a SAR heli while you maintain your standby for jobs you are equipped to do.
As I strive to remind our crews, knowing when to say no is the most difficult part of being in the rescue business - I think the addition of the winch to AA will make it far more difficult for your crews to do this.