Right, if you're not applying until next cycle, there really is no need to start on it now, you could I guess, but you'll have to update transcripts/what you've been doing for the background check, etc. The earliest I would start would be like tbond5 said, in July. I personally didn't start until October and have everything completed for the first board, but it depends on how quickly you and your recruiter can work to get everything in. 2 months to complete everything should be good if you are both on top of everything, but again the earlier the better in case you run into any problems (for example, with MEPS/however you do your physical, I personally did mine at Walter Reed where you get to keep much more dignity).
Also, to Jaesango, the application process is nearly identical. My recruiter just listed HSCP as my 2nd choice on my APSR. The checklist for the material needed for both are the same except for just a few minor formalities, but if you get the HPSP one complete, you probably have the HSCP complete as well.