You can/should absolutely start training for Denali tomorrow. You can never have too much base. If you have the time; then start now. 24 weeks is not some ideal time nor is it the MAXIMUM you should train. It is a reasonable compromise for most people and it gives them a decent amount of base for a climb like this. The way I would recommend extending that plan is to run through the first 3 months of the plan in August, September and October. This will give you a really good idea of the volume you can handle and how the training needs to proceed if you have never done a structured training program. This will take you through the 8 week Transition period and get you about 4 weeks into the Base period. This means that you can add 3 more months to your Base building. This approach will really only effect your strength progression. For strength I would keep the Max strength period at 8 weeks (starting in October and ending in late November) then shift to the Muscular Endurance phase of strength for 6-8 weeks (end of January). Then return to Max for 4-5 weeks (end of Feb) before putting in a final 6 weeks or so of ME. For aerobic volume progression; Just keep adding as you can manage the time and recovery.
I hope this helps,