Can I sell a coaching program that teaches raising money without tripping over securities rules?

Your instinct about the second structure being worse is pointing at broker-dealer rules. In general terms, US securities regulation treats transaction-based compensation for helping sell securities as the marker of broker activity, and interests in a syndication are usually securities. A flat tuition paid before any deal exists sits further from that line than a cut of the promote on deals you helped raise for. Neither is a clean answer, because how these rules apply to a specific fact pattern is a legal question, and this is exactly the case where you pay a securities lawyer before you publish the sales page rather than after. Getting the structure reviewed once costs less than the alternative.

The introduction problem is separate and quieter than the compensation problem. If your marketing says students get access to your investor list, you've made investor access part of what you sold, and the fact that the fee is flat may matter less than educators assume. Educators who teach capital raising tend to handle this by keeping the network side to peer introductions among students and refusing to hand over LP contacts at all. Less attractive in the ad copy, considerably simpler.

On the business rather than the legal side, teaching capital raising has a specific failure mode. Your student results depend on their deals performing, and you have no control over their deals. If a cohort member raises $2 million on the back of your curriculum and the deal goes to zero, their LPs will read your sales material during the litigation. Ask yourself what you want your program to say it delivers. "How offerings are structured and how sponsors communicate with investors" is defensible. "How to raise your first million" prices better and hands a plaintiff's lawyer a headline.

The promote-split version also breaks your incentive to tell a student their deal is bad. If your income depends on their raise closing, you'll coach toward closing. That's the part I'd worry about before the legal part.