Back up one step.
Simply stated, you want to work directly for the client. Period.
Explain to the client that you are there to satisfy his needs and wishes, and to work around his schedule. The GC cannot have both sides of the conversation between you and the client that guarantees the client gets what he wants. And if you work under the GC, the client will be paying the GC some 10% of what you'll charge... and for what? The GC is not qualified to be involved (unless you're clueless about construction or non-cooperative with other subs).

Back to your subject:
It is to our advantage to have clients pay for equipment in advance. There's nothing written anywhere that says it has to be that way. The AIA approach is simply putting the client at an advantage.

The only condition that I'm aware of where any kind of policy concerning equipment comes into play is that you can only ask for a certain percentage of a contracting job in advance. In CA where I live, it's 10%. That means that if your proposal is for equipment and contracting, you can only collect 10% of the total... obviously not enough to pay for the equipment.

My explanation to the client is straightforward: we are a custom house. We determine what equipment to buy for YOUR installation. We don't have a back room full of stuff we've bought that we have to force down your throat just to stay in business. Instead, we determine your exact needs, then order and supply that to you as a purchase. We then do the installation.

This keeps us from financing the client's purchase, and there is always some profit in equipment, so this helps us pay for our own and our hired labor while we do the job.