epsg.io
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Transform tool: input for multiple pairs of coordinates
Probably a long textarea replacing the two input boxes - with parsing of text done in JavaScript via regular expression.
Inspiration in: http://cs2cs.mygeodata.eu/
The "Switch X-Y" and "Include input coordinates" is a good idea as well.
First version of regular expression to be used for the coodinate extraction: https://regex101.com/r/jR1uN1/2
Geodetic and GPS are not yet picked, right?
No, not yet. Might be a bit difficult to do all this with one regular expression.