had an episode of psychosis - can I ever become a monk?

Good householder,

"Their website specifically says that if you have had psychosis in the past you cannot ordain or even go as a novice, since it would be a burden if your psychosis reappeared"

In short: that's the community's rule there, yet not something found as "Dhamma-agreement" in accordiance with the Dhamna-Vinaya and it's further not unusually that 'burdensome' get, out of compassion (one should be clear that there is not such as a right to ordain, but it's something which is given or not), ordained and maybe more a hint that not everything that carries fame in the world is really always worthy it.

Good, of course, to start associating, so that monks would know good householder good anyway and one should not think that people living at monasteries are generally viewed 'normal'. Yet not to speak of modern/western distinctions and SEAsians or even Dhammic. It's generally not so wise to prefer to seek a home in westernisationed/modernisationed communities but leave home first on a home level, into another nearby culture, nearby the heritage rather that modern.

In any case, good to not waste time and to use possibility to go forth, if one feels inspired and ways can be found.

Not only that outer conditions aren't for sure, intention and good aspirations are even more hindrances, as kusala isn't for sure and one is adviced by the Sublime Buddha to be there quick.

May good householder always remember that the Devas (not to speak of good and carefull monks) would open the doors for one after leaving home for the Noble Quest with a clear and honest heart.

And to pay approve of householder White clouds experiances in relation of heal. If the is a 'doctor' hwo leads to heal, then the Sublime Buddhha and his good disciples by use of the sublime Dhamma and practicing it. Medications of common ways may sometimes 'heal' for some time, sometimes not even that. Aging, sickness, death are sure, anyway, for one who took another birth. As for ending the wheel of stress, nothing else as the Noble path would really help.

(...and stop gaming of any kind! quick! nothing of permanent akusala cittas where one 'must' get 'stupid')

Answering this for personal experience. A few years back I was doing my Ph.D. in the UK and I got an episode of Psychosis, that turned into Schizophrenia, and I also got diagnosed with depression. My whole life turned upside-down and I had to return to my home country. I had no job and did literally nothing other than sleeping, for five years straight. Although I was on medication, studying Buddhism and Meditation helped me a lot, in fact, more than the medications.

Now your question. I can understand your condition like you want to do something that's defining, that will give you some sense of belonging and a task for the mind to achieve (forgive me if that's not the case).

I am assuming that you are either from the US or some European country. So before thinking to take ordination I will suggest you attend a few (2-3) ten days Vipassana retreats with S.N Goenka. Also, check for Zen meditation centers or retreats in and around you. Once you get acquainted with what it means to literally revolve your life around meditation and nirvana, you will be in a better position to have the courage to go-forth.

During the same time, spend a good amount of time studying Theravada scriptures to which the Thai forest tradition belongs.

If you are in Australia, you can go to the monastery of Ajahn Brahm who has studied in the Thai monasteries. Also, there are Theravada monasteries in the US. So, the good news is, you don't have to go to Thailand, maybe a good monastery is in your country.

I understand this, but where am I to go, then? Is there any school which sticks closely to the buddha's teachings, with a focus on meditation and the path of purification, where I can some day ordain?

I am still on medications and whenever I ask my psychiatrist to low down the medicine doses, he tells me that the psychosis episodes can repeat. So I cannot say with guarantee in your case, but there's always some sort of chance for it to relapse.

Or will I just have to live the rest of my life as a householder?

Being a householder is not that bad. Start small, reach the point from where there's nothing left other than going forth.