I checked Nevil Coghill's translation, where the relevant lines are translated as follows
Now I have told you shortly, in a clause,
The rank, the array, the number and the cause (...)
"In a clause" is not translated; the Norton Critical Edition and the Riverside Chaucer both gloss "in a clause" as "briefly". Preserving "in a clause" also preserves the metre and avoids using an obvious synonym of "shortly".
"Soothly" is also used in other parts of the Canterbury Tales, e.g. in line 117 of the General Prologue:
A forster was he, soothly, as I gesse.
In Coghill's translation:
He was a proper forester, I guess.
In line 468 of the General Prologue:
Gat-tothed was she, soothly for to seye.
In Coghill's translation
She had gap-teeth, set widely, truth to say.
In these two examples, "soothly" is interpreted as "truly, in truth" (see the Chaucer Glossary by N. Davis et al).
So where does "shortly" come from? The British library has a website where you can consult and compare Caxton's two editions of The Canterbury Tales. The 1476 edition says:
Now have I tolde you shortly in a clause
The (illustrated) 1483 edition says:
Now have a told you shortly in a clause
(There is only in difference: the 'e' at the end of 'tolde'.)
However, the Hengwrt manuscript renders the line as follows:
Now haue I toold yow / soothly in a clau{s}e
So it is a matter of conflicting sources for modern editions. For example, Nevill Coghill says in his translation that he consulted both Walter W. Skeat's seven-volume edition of Chaucer's works (Oxford, 1897) and F. N. Robinson's edition (Cambridge, Massachusetts, 1933), and that where the editions didn't agree, he made his own choices. This explains some of the differences between translations. If they thought "shortly" was authoritative, they may have thought it was repetitive (due to "in a clause"); if they thought "soothly" was authoritative, they may have wondered how to render this into modern English at all.
Update: R. M. Lumiansky's prose translation (Simon & Schuster, 2001) has the following rendition:
Now I have told you very briefly about the rank, the dress, and the number of these pilgrims, (...)
Lumiansky wrote in his introduction,
I have tried to reproduced Chaucer's phrases exactly, almost word for word, in natural, idiomatic, colloquial, modern English, which will convey to the modern reader the same effects that Chaucer's idiomatic Middle English conveyed to his audience.
(In this quote, "almost" is the operative word.)