Would OP’s proposed performance-based contract, where they’re only paid when the sale goes through, align their interests with yours better than the status quo model you describe here?

No, because of the second-order dynamics:

OP will have multiple clients. OP’s sales employees will get to choose which things to sell.

OP’s customer still has to do a lot of work to bring OP’s salespeople up to speed at all, and even more if they want to be successful/“compete” with OP’s other customers for OP’s salespeoples’ attention/effort.

It can be a good business model for OP if he can get it, but as has been mentioned elsewhere seasoned potential customers will not, and should not generally, bite.

The downside for OP is once the sales process starts working, his customer grows, probably hires in-house sales staff, trains them off OP’s work, and cuts his contract, so he is always having to work to bring in new.