OP - afraid I can't help with your specific situation. I will say, though...2% is pretty good. I base fixed fees on estimated construction costs, and it comes out to about 1.5% of construction costs for a typical building. (12-17% of the overall design fee, overall design fee is about 6% of construction costs). In your situation, I would tie it not to 'construction costs' but to the cost of structural components. This does two things - 1) if the owner decides to go with nicer windows or other non-structural upgrades that don't impact you, you don't unfairly profit from it and 2) you can get a bottom line number when your work is done. As soon as the structural punch list is done, you can put in your final invoice. Then have a provision to cover other incidentals hourly (the new windows need you to review a screw connection, signing the statement of special inspections at CO issuance, etc.).
human909 - I prefer fixed fee. My final work product provides value to the project. Whether that's the ability to get a permit, or find a more economical solution to a problem, or something...there is a cost to not having my drawings/letter/whatever. Figuring that out can be tough, but the AEC market in general seems to have landed on percentage of construction cost as a decent proxy.
So I try to balance that cost of not having my work (could range from a couple thousand dollars to not being able to build the building, which in turn could be a blank check's worth of costs because a business can't open, etc.), the time it will take to get it done and what I need to pay myself and cover other fixed or floating costs, and what my competitors may do it for.
The last one holds the least weight. As you said, this business is all about trust. Walking up to somebody and saying "hey, I'll screw over that other guy and do this for 80% of his fee" isn't a good way to engender trust...just makes you look like a sleazy cutthroat. But the market is the market, and if I price myself out of it I won't have any work. So I can't ignore it.
But as JStructsteel mentioned...if I've invested time and or money into building or purchasing design tools to make the project more efficient, I should be able to generate a profit from that investment. So you either have to keep raising your hourly rate to reflect it, or you charge the same lump sum fee and grow your margins as you spend less time on each one. While the hourly rate adjustment may feel 'cleaner' and even more ethical in some respects...it's not a great business move to constantly dial up your rates every other proposal. That will get noticed, and could alienate clients. But if I'm always doing the same job for the same price (indexed to construction costs), the client stays happy.