gdalwarp raster reprojection misalignment going to ESRI 102001?

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I am trying to convert 30 m spatial resolution rasters I have in WGS 84 UTM zones to ESRI 102001 using gdalwarp -tap -tr 30 30 -t_srs 'EPSG:102001' input.tif output.tif. The result is misaligned by 10 m (1/3 of a pixel) in the y-direction. I know this because I have a grid in ESRI 102001 and sample rasters that I am trying to align to (link to grid I am using: https://daac.ornl.gov/cgi-bin/dsviewer.pl?ds_id=1527).

I have tried various methods using command line gdal, python, and qgis, but I believe these all use gdal behind the scenes to do the projection... Attached are snippets of the metadata from gdalinfo for the example raster that is aligned correctly and a raster I reprojected, which is misaligned. It appears that the only differences are in the Corner Coordinates. If you subtract the y coords for corresponding corner coordinates (example circled in red) and divide by 30, it's not an integer number and corresponds exactly with the 10 m misalignment I see. The only way I've been able to fix this is by reprojecting again by taking the y extent and shifting by 10 m in a new gdalwarp command using '-te' for target extent; however, this is obviously cumbersome and impractical for me to do for a large number of rasters.

I am looking for any suggestions, preferrably using gdal or python, to reproject the raster so that it aligns correctly... and also curious about what's causing the issue!

Correct example raster info on left. Misaligned raster info on right.

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