Engraving Options has a setting for putting barlines ONLY between the staves, which is used in some critical editions** of early music editions. However, for this style, notes must not be split over the barlines, e.g. a whole note instead of two tied halves.
Is there a setting to allow Dorico to ‘ignore’ barlines in this way?
** But obviously, if I have to sing the thing, I want normal barlines and tied notes. 
I recommend getting used to singing this music without barlines and tied notes — it’s an easy adjustment, and you can get much closer to the way the composer actually wrote the music.
Thanks. I’ve been ‘getting used to it’ for 40 years. I actually find it easier to sight-sing directly from 16th-century partbooks than from Mensurstriche, because my mind is making different assumptions about the two notational styles.
Only if he wrote in imperfect proportion and time, otherwise you have to start compromising your ‘closeness’ with augmentation dots that were never there, and translating colouration. And you still have to tie notes over system breaks. And ligatures are not expressed verbatim, but broken up into modern conventional noteforms.
Its advantages are over-stated, and don’t outweigh the disadvantages.
As John Caldwell writes in his book “Editing Early Music”, no one is going to misunderstand the use of a tied note to convey what was originally intended.
There’s also an argument that ‘semibreves do not mean to me what they meant to Palestrina’. Any modern score is a translation, even if the symbols look broadly similar in appearance.
However, I am occasionally demanded to produce it, and there are also other uses for the same notational techniques in other areas. So thanks to Florian for the link.
You’re certainly right — I didn’t actually mean to suggest reading from new editions that don’t use barlines or ties — I meant reading from original editions. Plenty of old music is written in score format (each part stacked vertically, like modern music) and even with perfect tempus and prolation, it’s not too hard to get used to.
Partbooks present more significant difficulties in rehearsal, and I believe it’s not always practical to play from partbooks, although as you say, it can be done.