Sean, answering your specific last question, I've found multi-tier deals rarely work the way you hope.
The bigger fish who may not want to hit your threshold often push for it at half or three quarters of the step. The smaller fish often hold out or try to band together, formally or informally, adding complication and distraction to the fundraising process. If you discount through price you have to figure out what that means for liquidation preferences. (Is the pref at the list price or the discounted price? If I'm a whale I don't want the minnows to have a $1.00 per share pref when I get $0.80 per share.) Warrants often effect later rounds because they are a dilution overhang (but have not generated capital).
Similar issues apply on the "invest early, get a bonus" approach, whether it's a lower price (gee, what happened since last week that your shares are worth 20% more?) or warrants (same issue plus the dilution overhang).
Have fun - it's a common challenge when negotiating for capital.