The dealer pays a hell of a lot more than 60% of sticker price. That's kind of the point of "invoice". A dealer can still make a little profit on invoice, especially as it moves another car to help them make their sales figures (usually they get a payment per car if they hit X sales), but not always.

I worked for a dealership for a while. The key to making the buying experience painless is to do all the work before you ever see the car dealership. (I'll mention how this might not work in Hawaii as well at the end...)

• Pick out what you want for your car. DON'T say "I want a car with exactly these 27 options and no others". The more you limit your options, the more likely you will reduce the number of cars which meet your requirements, which means your chance of getting boned by the dealer go up a lot. Rather than looking for a lower trim level with exactly one particular set of options, consider a higher trim level with those options as standard - much easier to find.
• Definitely go to Edmunds or another site, know what the MSRP is, know what the invoice price is. Know what the destination charge is (they will charge you some money based on where you are, and you just can't do anything about that - they had to ship the car!)
• Talk to your bank, and get a quote on an auto loan. Don't actually take a loan yet, just know what you're approved for and at what interest rate. This sets a floor, a fallback position. If you go to the dealer and they can beat that rate, nice! Let them save you some money. If you've got an offer at 4% and the dealer tells you they can't get you done lower than 9%, you can tell 'em you've already arranged for financing. But either way you're no longer concerned about the budget - if you can pay the loan your bank offered, things can only improve from there.
• E-mail the dealerships in the area. Let them know what car you're looking for, what options you're looking for (keep that list small), and what colors you're interested in. Why are we doing this via e-mail? Most dealerships maintain an internet sales department (usually just one guy, heh). Internet customers tend to be high-information shoppers who are more resistant to the "usual" sales pitch tactics. If some faka sends you a quote for two grand over MSRP, and some other dealer gives you invoice, that first dealer will never hear from you again - and they know it. So the internet sales guy is there to get that kind of shopper in, get them in a car, get them out the door in the car, with much less hassle.
• This helps you avoid ambushes for "dealer added options". If they're actual things the dealership has done, they'll be rolled into the quote you get and you can just say "no thanks" from the comfort of your own house. If they're bullshit, it makes it quite easy to spot - you've already arranged for the price before showing up, so if you get there and that's not the price, walk.
• Look at your quotes, arrange to meet the internet guy at the dealership. Don't just walk in! They'll shunt you into the regular annoying sales stuff. Meet the internet guy and drive the car around.
• Assuming you like it, great! You've already worked out the price and you've got financing lined up. Tell the finance guy what he's got to beat and let him at it - if he can knock a few basis points off, hey, free money for you.
• If you get there and the deal isn't what you discussed in the e-mail, walk away. Don't argue it, -go home-. When you're in the dealership, the dealer will try to stretch things out to tire and annoy you into agreeing to stuff you might not want to agree to. When you're home, the power is all yours - they have to make you completely happy or you will never set foot on their property.

All that said. This works great on the mainland when you've got several car dealerships and can afford to tell one to take a hike because his competitors all have the same car. It might not work so well in Hawaii, especially on a neighbor island, because at the end of the day, the technique relies on competition to work. If there's no competition, it's not gonna work as well. Don't expect this technique to work well on cars in limited supply, cars with a lot of demand, or when there's only a single dealer with that car on the island. (If that's the case, look for more than one car - don't lock yourself into a decision and then discover that you have to go through McShifty's Screw-Yoo Motors to get that vehicle.)