Those Broads boats seem to be well sorted for short tacking, all the power is in the main, but they tend to be gaff rigged too
If yours is an older (1970's) boat with a skinny main and a big overlapping jib/genoa, I think you are stuck.
Newer boats seem to have a bigger main and smaller jib so going for a self tacker may not be too detrimental.
Are you on hank on sails? You could have both, keep the existing tracks for what you do now. Fit the self tacking gear for when you are short tacking up a narrow fairway.
I don't know about winching in 4 foot of sheet, we tend to be able to get most of it in by brute force and then winch the last foot.