Once ITM and blinds are ~100/200 (as you've suggested) if you have ~12-15 bb's, you don't really want to open raise with hands you're not willing to get it allin with ( you don't want to raise/fold preflop on a stack of this size). With ~20bb's you don't want to be open-shoving because you're risking too much to win too little (instead, look for spots where you can re-steal shove.. ie. if villain seems to be stealing alot, look to shove it allin over their raise with a stack of say 12-20bb, as your stack will be able to do significant damage to villain's stack & they likely won't call you unless on a decent hand (< this is player read dependent obviously).
On a big stack in late levels (once ITM) you'd typically want to adjust your raise size to 2.5xbb (instead of 3x) but again it depends upon the table (also depends upon 'effective' stack sizes, ie. if you're raising 2.5x into the BB who is sitting on 7bb, you might as well just shove on them preflop because you're not going to raise/fold to their smaller stack shove because you'll be priced in anyways, so just get it in first if you're planning on raising).
There are other variables (situational differences) involved once ITM in a SNG (ie. 2 bigstacks & 1 small, 1 big stack, 1 med. stack & 1 small, 3 med.-sized stacks, etc.,... also whether or not your opponents are playing too tight, or if they (or one of them) is playing very loose,... real aggressive, or real passive).
Think ahead in hands (ie. if you raise will you be priced in to call the villain's shove if they shove it allin over your raise, what about if they flat call preflop but then leave enough behind to shove the flop with ~pot-sized bet). Also use earlier player reads to determine if villain calls down wide. Another thing to consider is, "Is villain(s) familiar with ICM", "Does villain believe we are familiar with ICM", "Does villain seem to have knowledge of good shoving ranges". We need to make necessary adjustments according to how villain plays & the extent of villain's end-game play knowledge.