Which civvie model is most like the L1A1? G1? STG-58?

FAL's can come both full and semi auto so even a semi auto FAL is correct as far as it's original military set up.
DSA makes FAL's 100% in america but most FAL's are made from an original parts kit. Most any FAL you get was originally a military used rifle with a few parts swapped out with US parts so it can be sold here. As far as which ones are like their original military version = they are their military version minus the US parts. If a FAL was made from a complete matching parts kit then it is an original G1, L1A1, STG58 etc. minus the few US parts.
If the question is who makes the closest to original US parts then it depends on what receiver and what version of a FAL you would be going for. A couple countries used a unibrow feed ramp so Century receiver would be the most accurate copy for them. Some countries used different cuts on the receiver so depending on the version, one receiver may be closer to original than another.  

The closest to original would be a non US version that has never been taken apart but you will not likely find one like that.

SAR 48s are all factory original F A Ls made in Brazil and imported as complete rifles by Springfield Armory. 
 

Easy: Buy a rifle that was assembled with a US receiver and the parts kit of your choice.

Thanks.

If I'm looking at DS Arms for an L1A1 or an STG-58, which models would most similar?

if you are going for the classic FAL look, the STG58 would be close for the metric builds.

L1A1 is based on English pattern aka inch builds.