We actually do know that drugs that are considered "psychedelic" tend to have a dominant 5-HT2A agonist effect (serotonin targetting), actually. Chemical compounds are often not terribly specific, so other receptors get tickled as well... and there are other hallucinogen classifications that do not target serotonin receptors. But pretty much all of the "classic" psychedelics (ergolines and tryptamines) target 5-HT2A quite heavily; many phenethylamines also target 5-HT2A as well (although there is more receptor variety in that class of compounds).

I believe you are right that much of the overall effect on the brain of these compounds is poorly understood.