Both Miedema and Burns will have prospect camp the long weekend in July to show themselves. Usually, at the camp, the scouts will tell them what to work on so they are ready for rookie camp.
Burns will have a lot of people to fight against including Mayich. I see neither getting a signed contract unless the either the Blues or Sabres decide that there is something they show at the rookie camp. Attitude and work ethic over the summer will decide how long they stay in camps. None of these 3, personally, I think will last more than a week at the main camp at best because there is little chance that they will make the main team or the AHL team.
The player that you may miss the longest is Pie as he is eligible for the AHL, and they may want to see how he does at that level.