The Latin script is the most widely used script in the world. It spread primarily because of European colonialism. But is there any way to screw this script? How can I prevent the spread of the Latin script as much as possible with a POD no earlier than 1000 CE?
Screw Christianity in northern Europe and get more of a "pagan backlash" while simultaneously making Kievan Rus/Byzantium stronger. So you'd have West Slavs using Glagolitic and Scandinavians using some sort of runes and Lithuanians/Balts in general using one of those (or Cyrillic?). I envision they'd still be Christian, but they'd be very peripheral and end up with their own national churches.
And then screw Europe in general so no European colonialism. Let the New World and Africa be colonised by Arabs, or maybe divided between East Asians and Arabs if you want maximum diversity.
How can I, for example, get the Mesoamerican scripts to survive?
That's probably impossible since every script beside Maya is more akin to hieroglyphics and is difficult to use, although has the interesting principle that it's very semasiographic. IIRC it would have been easier for a literate Mixtec to understand an Aztec document than it is for a Japanese person to read a Chinese document. In some cases it isn't actually full writing but purely semasiographic. Historically these scripts tend to evolve toward being logographic, like Egyptian hieroglyphics, cuneiform, or the Chinese script (especially in Japan and Vietnam plus now-extinct scripts like Tangut).
Maya is rather different than it is an actual syllabary so would be easier to modernise. To a degree this was already occurring in the Postclassic. You just need to make the Maya wealthier and more widespread in the era after the decline of the League of Mayapan and then change the context of colonialism. For instance, Chinese characters don't seem to have been a problem for missionaries in China, so why not apply the same standard to Maya characters? Catholic missionaries in the Spanish empire were innovative in adapting native traditions from holidays to music to Christianity (Latin American baroque music commissioned by the church has a lot of native influences for instance, including choirs singing in Nahuatl and Quechua). So a stronger Maya being dragged into the global, connected world could maintain their script.
I wonder if it’s possible for some lesser-known Southeast Asian scripts like Baybayin and the Sundanese script to survive.
Problem is Islam + colonial era. You'd need some alternate way of incorporating them into the world system like a Chinese sort of setup where there isn't much direct rule but rather an expectation they pay tribute to the Emperor (including only enthroning rulers he recognises), and maybe some communities of Chinese merchants operating in the area. Since they're too distant to truly Sinicise, they'd retain a lot of their indigenous customs including their native scripts.
I think you'd need something like Buddhism rooting itself in the population, or maybe just Buddhism in general. Buddhism in that region appears to be an elite phenomena and never really reached the lower classes since you still had a lot of Hinduism and the traditional Southeast Asian folk beliefs. This was true in early Japan as well for instance, but in that country new sects of Buddhism appeared (i.e. Zen and various Pure Land schools) in the 12th-13th centuries which had both powerful local patrons and also incorporated enough local customs that gained a large following. You see similar things in Vietnam (where at one point a domestic school of Zen was sponsored by very high-ranking princes) and Burma where folk Buddhism was and is still very common in tandem with the more orthodox Theravada Buddhism of the elite. So I think it's possible enough to get the people there Buddhist enough that no ruler would ever consider converting and keep Christianity, Islam, or what not from achieving large numbers of converts.
It would be even better if you get the temples involved in commerce like they did in Japan, since a lot of Southeast Asia's conversion to Islam was driven by merchants+the ruler and his court converting. If commerce is being driven by temples of some state-sponsored/patronised Buddhist sect, then there would be less of an interest in converting to the religion of foreign merchants.