Yeah "tuning issues" with today's broadheads are pretty much a thing of the past. Aerodynamics have finally caught up with the speed demon bows of today. If your bow is properly tuned, then you will have little to no issue with a good fixed blade BH. But you need to stay away from the gimmic BH companies. Well respected companies include but are not limited to, Muzzy, G5, Rocket, Trophy Ridge, and a newer one on the scene Trophy Taker (T-Lock) has been getting outstanding reviews.
There is one very expensive broadhead set (pack of 3 is generally north of $70) that have started making a serious name for themselves in both accuracy as well as terminal performance. Solid Broadhead Legend series is basically a cut on contact 2 blade with little bleeder cross blades. I tested a pack myself and they did fly extremely well even at longer 60 yard ranges. Only shot one elk with them and it did the job quite well but I will admit at the range I hit that elk (3 yards) I could have gotten the same result with a blunt stick
So not much on the test. But it did lay her open and blood was everywhere for the 15 yards it ran.