We discussed the topic of who made the illustrations within Farmer Giles of Ham
in the threads Farmer Giles of Ham
and Tolkien the Illustrator
where we assumed they were also done by Pauline Baynes who did many of the illustrations in the Professor's books.
The editions of The Tolkien Reader
I own, and the only ones I have ever seen containing the story, are in the 1970 Ballantine paperback edition and the current Del Rey (Ballantine) edition, with the Professor's "weird hair" on the cover as shown in the link in Elanorraine's above post. Both my copies have the same illustrations. I have never seen this story in a hard cover edition, let alone a first edition.
Galin may have more definitive knowledge on this topic?