I've read that escargot can be a carrier of parasites (Angiostrongylus cantonensis) or bacteria that can lead to meningitis. I assume there are no visible signs if they are in fact carriers. Will the boiling process make escargot safe to eat if they are? I assume it's just a matter of time and temp but I want to be sure I'm not missing something.
I think you're a bit unclear what meningitis is. It isn't something like smallpox or salmonella, which are caused by a specific pathogen. Meningitis stands for an inflammation of the membranes covering the brain surface, and it can be caused by a number of pathogens. There is bacterial meningitis, viral meningitis, parasitic meningitis, and even meningitis where it isn't possible to find out what caused it.
As such, it is just wrong to say that a food can be a "meningitis carrier". If you want to say that every organism contaminated with a pathogen which can potentially cause meningitis is a "meningitis carrier", then everything is a meningitis carrier, including the lips of your significant other. If a significant proportion of contacts with a "meningitis carrier" lead to meningitis, humanity would have died out before it discovered fire. So first, you can't react to such news as to a statement like "escargot can carry salmonella". Second, if "meningitis carrier" was the real wording of your source, this is a red flag for its credibility.
If the material which you read says that "escargot is sometimes contaminated with bacterium X, which has been known to cross the blood brain barrier in a big percentage of infected people and cause meningitis", you should look up the combinations of time and temperature required for a 6-log10 reduction of this bacterium (the USDA publishes such data) and make sure that this temperature has been maintained at the core of the food for at least the time indicated. Just throwing into boiling water and waiting isn't enough, because you don't know when the core of the food reaches the temperature prescribed.
If your source doesn't mention the type of pathogen, you can't assume that boiling will kill it. There are bacteria on Earth which proliferate in hot geysers, and while it is unlikely that they can both live in escargot and cause meningitis, making the assumption that boiling can kill any pathogen is reckless. If the source was credible, you need to hunt more information, until you know which pathogen is meant, then follow the previous paragraph.
If your source wasn't especially credible, something like a tabloid saying "A child ate escargot and landed in hospital with meningitis! We will all die with our brains converted to swollen puss if we eat escargot!!!", then it was some common pathogen which happened to somehow reach a victim's brain in a single case. Disregard the meningitis scare, look up the guidelines for cooking escargot, and stick to them in order to eliminate the common pathogens contained in it.
edit: now you have updated your question, it was possible to do some research. The parasite was the easy one.
This paper is used as a basis for the safety guidelines of some government organs, e. g. the public health agency of Canada: link. As it doesn't say how the 2-3 minutes are measured, I'd wait until the core of a snail is at 55°C, and measure at least 3 minutes after that (or more, for added safety). This will make you safe from the parasite infection, which sometimes causes meningitis (and is probably unpleasant even if it doesn't reach the brain).
As for bacteria, I didn't find any special information about escargot or any kind of land snails. As all the mentions of escargot and meningitis together I found pointed to the parasite as a cause, there probably isn't an escargot specific bacterium which causes meningitis or other unusual illness. So the usual food safety guidelines apply. Sadly, the various food safety organs of different countries don't seem to have published specific guidelines for escargot (maybe the French have, but I don't speak French). You can use the guidelines for seafood, because for food safety purposes, escargots count as mollusks Foodsafety.gov is a good place to start for the home cook - even if you don't live in the USA, you can trust them to have chosen good guidelines. The FDA site also contains good information, it lists 145°F internal temperature for seafood, but, strangely, no time period.
A. cantonenis is endemic in mostly tropical and sub-tropical areas. It can be in other spots though this is extremely rare. That said, by far the most escargot in the US is canned, so previously cooked, and them must be heated again before consumption. Getting infected with A.cantonenis, and therefore the possibility of getting meningitis, would be a one in a million shot---you're more likely to get sick from grocery store chicken!