There is some arcane method for determining from the element description what sort of replacement chit it uses
It does seem that way sometimes, but it has more to do with some misleading descriptions. This is more technical than some people will care about, and many already know it, but whatever.
Individual elements have families. Artillery in CW2 uses ones of three families, famLightArty, famMedArty and famHvyArty. There is an additional family (maybe more) that exists in CW2 that no element uses, famSHvyArty. It's not defined in the family aliases .ini, but I've added it in mods and it works with no issues. Classifying some artillery elements with famSHvyArty would have made sense and made replacement costs more manageable. I don't know why the developers decided not to.
The family names are aliases and they resolve to numbers that the game uses. They are built into the engine and you can't modify them other than to change their string descriptions. Their string descriptions are stored in LocalStrings__AGE.csv in the Settings folder, and it's the string descriptions that you see in-game on the relevant tab. famLightArty has the string description "Light Artillery" (depends on the language), and so on.
When an element needs a replacement, the replacement chit it draws from is decided by the element family. The cost of the replacement chit often doesn't exactly equal the cost of a completely new battery of artillery because the cost of the replacement chit is an average of the costs of all the types of elements for a faction that are in the force pool and/or on the board. Most of the artillery units are using the same model. If you have horse artillery from AR, LA and VA in the force pool, the game still calculates the average using their common model type, which is mdl_CMN_Art0. Another common model is mdl_CMN_Art1, CSA 6lbers. Both of those models use the same family, famLightArty. Once both types are in the force pool or on the board, the game takes their costs and divides by two (two model types with famLightArty). That will be their replacement chit cost. Note that it is specific to faction. The game doesn't average costs of artillery for all the factions and give a single replacement chit cost to all factions.
The cost of replacement chits can change over the course of the game if new elements are added to (or removed from) the force pool. In the April '61 campaign, initially there is only one type of CSA "light artillery" on the board or in the force pool, and that's the 6lber. CSA light artillery replacement chit costs in April have only one type to calculate the average (mdl_CMN_Art1) and replacement chit costs the same as it does to buy a new 6lber ($20/5 WS). When more expensive horse artillery, also "light artillery", is added to the CSA force pool, it drives the average cost up, and the replacement cost goes up ($21/6 WS, conscripts are the same). On the other hand, CSA medium and heavy artillery replacement chit costs go down after the first month of the full '61 campaign. You'll save a few CSA bucks and war supplies by buying light arty replacement chits in the first month, medium and heavy arty later.
How artillery was classified during the conflict does not equate to how it is defined in the game. In the game it has more to do with costs. For example, 20lb Parrott rifles were considered field artillery, but in the game they are classified as heavy artillery. If the game classified 20lb Parrotts as "field artillery" (famMedArty), it would drive up the costs of the field artillery replacement chits.
*Correction* I am wrong for the same reason that Orso is wrong/right. The *model* for the CMN faction model 20lb arty is using famHvyArty, but the *unit* file that calls it in-game redefines it as famMedArty.Fort artillery is medium artillery.
My unmodded game (v1.06) says "Heavy Artillery" on the element descriptions for CSA and USA fort batteries, but I went ahead and looked into it. There are two CMN faction fort artillery models that both use famHvyArty. There are CSA and USA model files that use the CMN faction fort artillery models as templates, but redefine the family as famMedArty. However, the units that are called in the game are using the CMN faction models, and further specify famHvyArty in their unit files.
Fort batteries are famHvyArty, "Heavy Artillery".