freelance short term lecturing work

[maria24 0]

I am a UK citizen and resident and plan to teach highly specialised CPD courses in the US. Each course is held over four 3 day weekends (i.e. 12 days). Ideally I want to teach on both East and West coast, so plan to fly in four times for 2-3 weeks over a period of about 12 to 15 months.
I have many US students who ask me to come to the States to teach this particular course. I teach it in the UK to an international audience regualrly, and they want me to come to the US as many cannot travel here regularly. the course i accredited by US professional organisations,a s well as European and Australian ones.

I attend international conferences and teach shorter 1 - 3 day modules at universities allover the world (including USA) at times.
Now I am trying to figure out if it is possible to do this without an American host inviting me, and to set this up freelance. Bookings can be made online directly through my UK website, so I do not need to receive a salary in the USA, and I would finance all my travel etc myself.
What visa do I need, if any?

Is it possible that I would be refused entry after coming in twice, for example, and therefore could not guarantee the continuity of the course?

Do I need an invitation?

Can I sell services and take payment online in the UK and then deliver the services in the USA?

Do I need to pay someone in the US a fee to host me and set up the course and invite me (I would prefer not to do that)? What visa would I require then?

What restrictions apply?

I owuld appreciate any answers, or advice how to get them, as I don't seem to be able to find a defintive answer.

Thank you all!

[Boiler 45,911]

Nothing comes to mind freelance.

Going through a US Uni should be doable.