It was interesting read but I do have a question though speaking in general.
What are the chances that these amphilophus are crossbreeding in the wild if there is (for example) 4 different types of amphilophus in an area?
Juan Miguel Artigas mentioned once before that the parachromis multifaciatus is actually a crossbred between a Jaguar and something (can't remember) as Jaguar cichlids were introduced into Southern Mexico to cull out the population of tilapia in the waterways for fishermen.
Not P. multifasciatus, that's an actual species with a unique genetic identity. You're thinking of the weird La Ceiba ones, which a bunch of people think is either a hybrid that was made as a result of in introduction, or a new species. Bottom line is we won't know because the body of water they were caught in was drained and dredged to build a hotel. Juan Miguel I will say has had some... interesting ideas about taxonomic classifications though recently, one of his most recent ones being that Thorichthys meeki/affinis/panchovillai are all the same species... based on morphology and behavior. This was disproven 10 years ago by a study that used "three nested taxon sampling analyses of the concatenated nDNA/mtDNA datasets and additionally to these analyses we present a summaryof the results of a new Next Generation Sequencing-generated nuclear phylogeny based on a data set of ~ 140,000 informative characters." (Rican et al. 2016). Another being him citing his own hobbyist magazine articles as formal "published" taxonomic revisions (e.g him "formally" synonymizing Amatitlania siquia and nigrofasciata based on a 2017 study that said not do revisions based on their data because they only used mtDNA and didn't do an IQTREE or something).
Systematic semantics aside, I personally think P. sp. La Ceiba (given it is a hybrid) is a hybrid of multifasciatus and motaguensis. The proposition you've probably heard is that it was a hybrid of managuensis and motaguensis (as motaguensis is the native one), but multifasciatus allegedly has also been introduced to the area, and a managuensis hybrid would look VERY drastically different. Not to mention the fact that motaguensis and managuensis naturally overlap in MANY other areas in Honduras, and we haven't found the La Ceiba type fish again anywhere else. I will say Honduras has a lot of weird stuff with mutations and "unidentified" fish like that because the Honduran Red Point "blue" gene is also a recessive mutation like the electric blue genes in jack dempsies and blue acaras. There's also an isolated population of rainbow cichlids in Northeastern Honduras and an undescribed Cribroheros.
As for Amphilophus crossbreeding, inherently there is the chance but with so many relatively new lineages of cichlids evolving sympatrically throughout Central America in general, they evidently have certain "barriers" that work against the desire to hybridize despite their ability to without issue. If there are 4 lineages that are as distinct as they are in their mitochondrial DNA then there is little evidence of them hybridizing.
Mitochondrial DNA is generally not the best for species level phylogeny (especially in recent diversifications with very closely related species) because sperm does not have a mitochondria, so while mitochondrial DNA has the benefit of being a quick cheap and easy way to spit out phylogenies (given you're doing the genetics of a microorganism as opposed to the animal itself), mitochondrial DNA is only passed down from the mother's side, so any recent hybridization events will show up as homoplasy with the most recent ancestral "mother" species in the DNA.
One big example of hybridization (especially in Amphilophus) though is Amphilophus istlanum, which as evidence would suggest, evolved stemming from a hybridization event between Mayaheros beani and Amphilophus trimaculatum (though I do share the sentiment with Juan Miguel that there is maybe a chance of trimacs/lyonsi/istlanum not actually belonging in Amphilophus, though his basis for this claim is that the genus has never been diagnosed, which again is not true given the aforementioned 2016 study). Istlanum essentially just happened to have more genes from trimaculatum so that's why it stayed in Amphilophus. There's a few others though, like the main reason Nosferatu got lumped into Herichthys is because they found that there's thousands of years of gene flow between the cyanoguttatus group and the Nosferatu group. Essentially they probably would've been separate if they didn't do that.
Most hybridization events from what I've observed in nature (and in tanks) is that hybridization only really occurs out of "necessity" or just becomes more statistically likely if not enough of one species is available. E.g with the La Ceiba "freddies", or my local creek, which has introduced green sunfish and native longear sunfish, but there is about a 20 to 1 ratio of green sunfish to longear so there's an equal amount of longear x green sunfish hybrids as there are pure longear.
As mentioned though sometimes sympatric species have barriers to reproduction, like in the case of a lot of Central American cichlids that occur alongside their close relatives (particularly Amphilophines), generally behavior does segregate species from eachother, such as in the case of Amatitlania throughout Costa Rica and Panama (most rivers with Amatitlania have 2 that segregate based on flow of the river), or obviously in Amphilophus, with a more clear example being the ones in Lake Apoyo or Xiloa where they have more clearly separated ecological niches that keep them away from eachtoher. Obviously we don't really know enough about the Lake Nicaragua ones to be able to tell what physical means they're using the stop from breeding with eachother, but evidently there is something.