"shortest route" and "straight line" actually mean pretty much the same thing. The shortest route is the straight line. Sorry if I confused the matter by switching up the terminology.
Flying parallel to the lines of latitude would mean that your bearing doesn't change much, sure, but flying in a straight line would require your heading to change continuously.
The aircraft in the screenshot was flying a very not-straight course
BGA, like in the photo, isn't the only option. There are options only slightly larger with hand-solderable packages (if you're good at soldering)