>> strategy of bidding high to get a very high CTR and high QS so that your CPCs start to reduce over time.
That's not how it works. Bidding higher will get you in a higher position but the QS is calculated based on relative CTR for that position, not absolute. In other words, a poor ad will get a poor QS no matter its position.
>> Also conversion rates are higher the further you are up the page.
Click prices in PPC are driven by market forces. You have to bid a certain amount to be where you want to be (at the top) because that's what that market dictates. Lawyer keywords for example are more expensive because it's worth it for them to pay $10, $20 or more.
Getting back to the higher up the ad is, the better the conversion, why don't you bid more to get there? You often don't pay that much more. What I mean is, doubling the bid doesn't mean a doubling in CPC. And the extra sales may make it worth it. What you have in your favor is your QS which you say is excellent (I take that to mean at least 7) which indicates you likely have the right keywords so no need to weed any out. If you're not willing to bid any more, then improve your ads, something you should always do anyway.