jpeg is a container format like tiff, and the mpeg formats so there are various options which probably aren't implemented in your camera firmware.

JFIF & EXIF metadata types are incompatible with each other - a file can have one or the other.

Image encoding methods have evolved so the jpeg "standard" as used by old codecs and devices may lack features used in newer software. Progressive encoding was a later addition to enhance web use for example.

I did a bit of sleuthing with exiftool on the images you supplied and these are what I'm seeing as the most relevant information from the camera output.

Exif Byte Order                 : Little-endian (Intel, II)
...
Compression                     : JPEG (old-style)
...
Image Width                     : 1600
Image Height                    : 1064
Encoding Process                : Baseline DCT, 
Huffman coding
Bits Per Sample                 : 8
Color Components                : 3
Y Cb Cr Sub Sampling            : YCbCr4:2:2 (2 1)

In your failing file...

Exif Byte Order                 : Big-endian (Motorola, MM)
Image Width                     : 633
Image Height                    : 525
Y Cb Cr Sub Sampling            : YCbCr4:2:0 (2 2)

The first of these will be pretty good at tripping up a decoder that is probably only built to decode files it created, and image height/widths that aren't a multiple of 8 can be a known issue for older devices.

ImageMagick is probably the tool you need here - it's a command line tool where you can be quite detailed in how you want the file to be encoded, you'll need to look through the docs to set the right options. Or you can get exiftool and play around with all the encoding options in your software until you get it matched up.