I'm familiar with the rules of schach in general, but specifically, can I use pressure-treated lumber for schach? (We're looking to make a rollable "mat", like the reed ones, but out of 1x2 or 1x3 lumber)
According to the Rambam, who is basing himself on an explicit Mishnah and both Talmudhim (i.e. Bavli and Yerushalmi), it is completely mutar to use such lumber.
In Hilkhoth Sukkah 5:6-8 (according to the numbering of the Yemenite editions), the Rambam writes that it is permitted to use the shafts of arrows as sekhakh, as long as they are the "male"-ended ones, rather than the "female"-ended ones - into which an arrowhead can be placed - since it then is considered to have a bayith qibbul and is therefore subject to tum'ah. Substances subject to tum'ah is one of the invalidating factors of sekhakh (cf. Hilkhoth Sukkah 5:1).
In 5:8, the Rambam says explicitly that planed boards are valid for use as sekhakh, as long as either their width or thickness does not exceed arba` tefahim (approx. 12 inches) since boards wider than that could be mistakenly construed to be like a roof (i.e. bal tiqrah) and people may mistakenly reason that they can be yosse yedhei hovatham by sitting in their own homes. Whether they are pressure-treated or not does not seem to have any bearing on their viability as sekhakh. The treating of wood with oils, saps, and other substances is very ancient in the history of wood preservation. The need to keep it from rotting, decaying, or being eaten by worms - and thereby weakening - was of central importance. See here for a discussion of various practices. Since it seems that wood treatment was common in the times of Hazal and the Rishonim, and they did not mention it as a concern for the use of boards and arrows as sekhakh, it seems that we do not need to take it into account either.
This type of sekhakh, especially that of furring strips as you describe, has come back into use recently and many in both Eress Yisra'el and in the Golah use them.
While it is true that the Shulhan Arukh was mahmir and brought the shittah of the Semag that since roofs in his time were made out of such planed boards, one should not use boards for sekhakh, lest it be seen as a roof (bal tiqrah) - in our times roofs are made of plywood, plaster, shingles, etc. and one would not become confused by such boards any longer. This reasoning was given to me by several of my teachers - may they live and be well - regarding this question.
See the `Arokh HaShulhan, Hilkhoth Sukkah, Siman 629:31-32 for a discussion of the relevant sources and the opinion of HaRav Epshtein z"l regarding the issue of use of boards and planks of all widths - there he seems to go even further and prohibit the use of even thin strips of wood due to the fact that to him (apparently in his locale in Lita) they appeared like a roof (i.e. bal tiqrah), however the Rambam's clear statements in 5:9 seems to alleviate these concerns which have their origination in the words of the Semag and not Hazal at all, who even permit one to sit in his home as long as he detaches the roof boards of his house from the walls, they (of course) meet the width requirements, he resets them over his house, and the boards do not have any plaster or mortar on them.
To answer your question specifically regarding the mats, such mats are explicitly permitted when made out of qanim (cf. 5:7), but there is no indication that the use of narrow boards would be any different. To the contrary, le-`aniyuth da'ati, since cane mats made for sleeping or lying upon are not kosher for sekhakh since they retain the status of a keli, a mat made from thin boards would be all the better since no one uses such "mats" for any kind of sitting or lying at all - making it plain to all that your intention is for sekhakh alone.
Just make sure that the twine you use is a completely natural substance that is approved of by the modern poseqim for such purposes.
Hope this helps. Kol tuv.