From the answers that I got over here, I found out that the type of puzzle that I was looking for would be referred to as diagramless fill-in puzzle. (A cross of a diagramless crossword and a fill-in puzzle.)
Some Penny Press puzzle variety books have one or two of the diagramless fill-in puzzles. I also like them and have a hard time finding them. For the Penny Press puzzles, they have a list of words and only the e's are in the diagram. You have to determine the correct position from that.
Believe it or not, there are two books of Diagramless Fill-Ins (I have both of them myself) that exist. You can purchase both of them on Amazon.
The last puzzle in each book is different (in the first book, it's a diagramless fill-in where you get all the O's instead of all the E's. In the second book, the final puzzle is a diagramless crossword).