1) I edited my post above to include
num=`convert lena_*.png -format "%n\n" info: | tail -n 1`
where in my case num=4
See
http://www.imagemagick.org/script/escape.php
2) Montage will also degrade the quality. Adding -quality 100 will still change the quality.
If you name your files in the correct order with leading zeros, then you can simply montage them if you know the tile arrangement. But that would only work easily if the image is square. That way you can take sqrt(num) for the number of row and columns in -tile RxC.
Or you could precompute how many rows and columns you will get by dividing the input dimensions by your crop dimensions. Then you could just montage with -tile RxC.
Or you could use my script, overlay-crop, with zero overlap and label them in matrix format. Then parse the labels of the last image to find how many rows and column. Then use montage to combine together again. See my scripts at my link below.