Do lien waivers per draw actually protect me from the GC's subs, or just from the GC?

A waiver binds the party who signs it and nobody else. The GC's waiver on draw three releases the GC's claim for that work, and the plumbing sub who wasn't paid still has whatever lien rights the statute gives him, because the claim runs against the property. So your instinct about paying twice describes the actual exposure.

The mechanism operators use is a waiver from every party with lien rights above a threshold you set, subs and material suppliers included, collected as a condition of each draw rather than at the end. Conditional and unconditional matter in sequence: a conditional waiver takes effect once the payment clears, an unconditional one takes effect on signature whether the check is good or not, so you generally hand out conditional forms with the check and collect the unconditional version after funds clear. Joint checks made payable to the GC and the sub together are the blunter tool, and they slow your draw cycle down because two signatures have to be gathered before anyone deposits.

Preliminary notice, where a state requires it, works in your favor as information. It's how you learn a framing supplier you never contracted with is in the chain. Lien deadlines, notice requirements, waiver forms and whether statutory language is mandatory all vary by state, and several states publish forms you cannot modify, so have a construction attorney in that state build your draw package.

The failure that catches people isn't draw three. It's the final draw and retainage. Hold back 10 percent until you have unconditional waivers from everyone and the title company is satisfied, because an unreleased lien discovered in escrow stops the closing, and on a gut already running 130 or 140 days you're funding another month of interest, insurance and utilities while a bond or a payoff gets sorted.