No, there is no trick. You can "apply for GC" anytime, before after at the end, whatever. All that you need to do is submit I-485 with at least 5 months left on one's TN, at which point you switch to EAD, which is simple. There is never a need to apply and get it all finalized under the same TN term. You never need to apply for H1.
It does not become faster under H1. It just removes any timing worries.