It is properly understood according to the one who maintains that the boards were one אמה thick at their bottom and would continually narrow down until an אצבע, etc. - הניחא למאן דאמר קרשים מלמטה עוביין אמה וכלין והולכין עד כאצבע
They could not place the narrow side of the קרשים next to the wide side because a) it is a גנאי, b) it was too difficult, and c) it narrowed after the midpoint. We derive the status of a רה"ר from מחנה לויה, we derive from the עגלות who were in a רה"ר merely the size of a רה"ר (sixteen אמות).
Where did he place the אטבעי, on top of the wagon; but the wagon was covered - אטבעי היכא מנח להו אגבא דעגלה עגלה מקורה היא
The אטבעי of רב כהנא and the יתידות of שמואל are both referring to the punctured wood which are placed as a base to the length of the עגלה on which to place the קרשים; however initially we mistakenly assumed that רב כהנא meant the woods which we placed to the width of the עגלה, as a bracket, to prevent the קרשים from falling off the עגלה.