An Undeciphered Transposition Cipher of William Perwich, an English Agent in Paris (1670)

An undeciphered ciphertext in a letter from William Perwich to Lord Arlington, Paris, 9 April 1670 NS (TNA SP78/129, f.180) is presented in a blog post of The National Archives (TNA). (I thank Norbert Biermann for drawing my attention to this last month.) It appears to be a transposition cipher, given the letter frequencies as well as the occurrence of abbreviations such as ye(=the) or yt(=that).

My transcription of the ciphertext is here, which is slightly different from the version given on the TNA blog. I grouped some letters (e.g., "QR" on the first line and the second last line) but I'm not so sure of this. Actually, without such grouping, there are exactly 500 elements (excluding the last "likelyhood"), which is plausible in a transposition cipher, suggesting a transposition matrix of 25x20, 20x25, 10x50, etc.
Assuming columnar transposition (a Dutch example from 1675), I (manually) tried various matrix sizes (not limited to the factors of 500) and looked for matrix dimensions that might allow transposition of columns (or rows) to align Qs and Us, but it was not successful. (I assumed transcription of Q and U was correct.)

The TNA blog points out a possibility that this employs Samnuel Morland's scheme (see my article quoted therein) used by some English diplomats at the time. Indeed, Sir William Temple wrote in 1669 "Mr. Perwick wrote from France for a Tryal between us" about "Sir Samuel Mroland's Cypher".
Actually, the transposition scheme proposed by Samuel Morland is not limited to rectangular matrices, but can employ a triangle, a pentagon, a hexagon, or even more irregular patterns. But considering that "ruled papers" were supplied, I think use of non-rectangular matrices is not likely.
We may consider various patterns for inserting nulls by studying known examples.

The letter is calendared on p.82 of M. Beryl Curran (ed.) (1903), The Despatches of William Perwich, English Agent in Paris, 1669-1677 (Wikimedia Commons), which silently omits the paragraph in cipher. (The first paragraph of the letter belongs to another letter in the calendar from the same date addressed to Sir Joseph Williamson, with some difference in wording. Probably, the calendar omits such repetition to different recipients.)