Batch Reproject many Geotiff files into individual projections with calculated pixel size

I have many Geotiffs in LatLon WGS84 that I need to reproject in batch to individual projections (LCC with custom SPs and CMs).
On top, I need the resulting files to have the arithmetic mean pixel size of the suggested (or calculated) values for X and Y.
Not being familiar with GM scripting, I saw that I can manipulate the projection, so I can probably get around that.
However, is there a way to also calculate the pixel size as needed?
Thank you very much in advance.

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