If this is your first H1 (the initial 3 years)
then you still have 3 more years without any special requirements. If you are finishing 6 years, then you can extend your H1, one year at a time, if you have started your GC process atleast 1 year before H1 expiration AND your labour certification has been approved. I got mine done this way. I have heard of cases where the lawyers have been able to successfully make a case solely on the basis of having applied 1 year before expiration of H1 (without LC). So bottomline, you can wait till about a year before your H1 6 years expires. The big question obviously is why would you want to wait ? For GC, earlier the better. There is no saying how immigration laws, processes, etc will change, leave alone the job/economic front.