Revised: Don't require the seek call:

s3_r = boto3.resource('s3')
profile = source_image.profile.copy()

with rasterio.io.MemoryFile() as stack:
    with stack.open(**profile) as stack_out:
        stack_out.write(source_image.read(1), 1)
    s3_r.Object(<my-bucket>, <my-key>).upload_fileobj(stack)

For reference, doing:

s3_r = boto3.resource('s3')
profile = source_image.profile.copy()

with rasterio.io.MemoryFile() as stack:
    profile['driver'] = 'GTiff'
    with stack.open(**profile) as stack_out:
        stack_out.write(source_image.read(1), 1)
    s3_r.Object(<my-bucket>, <my-key>).upload_fileobj(stack)

results in a correctly geocoded GeoTiff. Appears it is an issue with .jp2s and Profiles/MemoryFiles.