Question 1: What determines how long this "wild spending" needs to be continued? Is it a matter of time? Or of impressions? Or something else?
Question 2: How will this effort be affected (if at all) by setting the the daily budget for this new Ad Group to a low enough $ level so that the ads are served only part of the day? (And would the portion of the day matter? I.E... 4 hours/day, 12 hours/day, etc.)
What I do is wait for every approximately 100-200 clicks. I then look at the actual CPC column. It will obviously be lower than your max CPC you're willing to pay. As your CTR increases this actual CPC gets lower. Reset you max CPC just above (maybe 0.01 or 0.02) the actual.
Improve. test your ad copy..
Wait another 100-200 clicks and adjust again. I've found that as long as your max is above your actual, then you shouldn't lose your position.
Using this approach, I managed to reduce my CPC down to an average of 0.03 per click for very competitive , highly searched health insurance related keywords and I average 4.0 placement in the ad group.
Try it out while , of course, always trying to improve your CTR with better ad copy along the way.