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Firstly, sorry for having to post this question, I feel like I've been going in circles trying to make sense of similar questions. I'm quite new to QGIS so please do re-direct this if needed.

Why I want to do I want to crop the NLCD data raster, e.g. Raster -> Extraction -> Clip Raster by Mask Layer so I can do some very basic counting of land-types on a per-county basis. This in itself seems to cause issues as the Raster data is just so big. So if there is some other method that I am unaware, please let me know. Otherwise, please read on.

Background: Like many that have come before me, I have been using the NLCD Land Cover CONUS Data set for the US. This provides a pretty large set of files (~20 GB per year), of which a erdas .img file is easily created in QGIS (drag and drop). In the metadata file, this has the projection:

PROJCS["Albers_Conical_Equal_Area",GEOGCS["GCS_WGS_1984",DATUM["D_WGS_1984",SPHEROID["WGS_1984",6378137.0,298.257223563]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Albers"],PARAMETER["false_easting",0.0],PARAMETER["false_northing",0.0],PARAMETER["central_meridian",-96.0],PARAMETER["standard_parallel_1",29.5],PARAMETER["standard_parallel_2",45.5],PARAMETER["latitude_of_origin",23.0],UNIT["Meter",1.0]]

Next to this, we have the US 2017 Census County Shapefiles. Again this is easily entered into QGIS with a drag and drop. This has the projection:

GEOGCS["GCS_North_American_1983",DATUM["D_North_American_1983",SPHEROID["GRS_1980",6378137,298.257222101]],PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]]

Problem Summary: Default QGIS CRS is 4326. I load in the NLCD data, set the NLCD layer CRS to EPSG:102003 (Albers). I then set the project CRS to the same. Then loading in the Shapefiles for the US County data, I get the image below. Showing that the layers are offset.

NLCD Data & Shapefiles Layer

I feel like the issue could relate to the problems as described here and here but I'm not exactly sure what is going wrong in my process. Further, my data is so big that any warping seems to take forever on my laptop.

Am I just missing something obvious?

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