A HOD should make it to SEO1 relatively easily, which maxes out around 9k. Most will move up to SEO2 (10k) and maybe even SEO3 (12k?) by retirement, even without going up the ladder further.
At SEO level it gets harder to get high performance grade, since you are ranked against other appointment holders. Assuming you really cap at HOD level, let's assume you'll be an average C grader. (I've heard that PB quantum is higher for SEOs, but I don't know the exact figures there). Assuming a more conservative 16 month package, at the SEO1 ceiling that's still about 140k per year. The annual cap could exceed 150k once you hit SEO2.
I'm not that familiar with private tuition industry, but I imagine it's hard to top that unless you are a star tutor, and possibly only if self-employed. Overall I imagine private might net you more $/hour - a major trade-off would be less stability as compared to
MOE employment.
You'll probably need to do more research to investigate potential earnings in the private side (or maybe someone more knowledgeable can share?), but your personal job satisfaction should play a part here. Some people I know value the greater focus on teaching within the tuition scene; some prefer the hours; others I know feel a mission to do their part contributing to the public system (cheesy but true).
(Re: your initial question - Saikang projects, if executed well, will help demonstrate your ability to manage resources and timelines. This should, of course, be on top of your core classroom/CCA duties. If you're ‘hungry’, I suggest just being upfront with your RO about wanting more opportunities to learn more. If you're competent enough, he/she should appreciate having a reliable officer to task things to while simultaneously being groomed for further responsibilities.)