When I chinned on my tank, I used void and eagle eye w/ extremes. I wasted a lot more prayer pots but you are effectively increasing your damage by 20%+, therefore you only use 20% less chins, which is much cheaper than more prayer pots - not to mention faster. I used grand tree pods for fast banking also. Guides will tell you to use high pray bonus, ignore that and go for range bonus/range damage, it saves more money and is faster.
With void and good gear and extremes I would say 25-28k chins