The Peyote Way Church of God is an Arizona based non-sectarian organization offering a Spirit Walk that requires 24 hours of fasting followed by a solitary peyote experience in natural surroundings. There are a number of states that do not restrict the use of peyote when used as religious sacrament, either within the Native American Church (NAC) or similar religious organizations. The current US states that allow this outside the NAC are AZ, CO, MN, NV, NM & OR, with various others allowing it for members of the NAC.
Similarly, various ayahuasca experiences seem to be available in the United States through the Churches of Santo Daime, UDV (Uniao De Vegetal), and the NAC. There does not seem to be much information available directly online, you would probably need to contact some of these groups although I'm not exactly sure how, it seems you would need to know a member.
Here is a short documentary about a Santo Daime church in Ashland Oregon. The church is known as the Church of the Holy Light of the Queen, as mentioned in the article The Holy Dose: Spiritual adventures with Southern Oregon's psychedelic crusaders. The Santo Daime experience, at least in Ashland, comes with quite a bit of ritual, special clothing and chanting.
The UDV is apparently happening in Colorado, New Mexico, California, Florida, Texas, and Washington. Santa Fe's UDV church has been mentioned in the news.
Ayaquest offers an ayahuasca ceremony which I believe is in Kentucky and within the NAC.
In the past there has been a Church of the Sacred Mushroom although the link seems to be dead. To me, this seems like something that we should be doing in the sense that the mushroom experience takes one to a similar territory, is not as puke-inducing as ayahuasca or peyote, and it fits into a slightly more manageable time frame. But, to each their own.
At any rate, there are many alternative experiences and treatments available, even with the US. For example, I recently heard of someone looking into ketamine treatments for depression. And outside the US, ibogaine treatments are available.
Soulquest Ayahuasca retreats in Florida