Sheil, if your 2 hour post-meal reading is 12.7 and it will come back to within normal range without any short acting insulin, then I'd suggest that your basal insulin is incorrect. Before and after meal readings should be consistent with each other; and your after meal reading and the next before meal reading should be broadly consistent too. To figure out if your basal is correct you need to look at your overnight readings. You say that your pre-breakfast reading was perfect. Was there a difference between your bedtime reading and your breakfast reading?
Also, what was it you ate for breakfast? Could be that the food you had was high in GI, but by 2 hours a high GI meal should have been taken care of with your insulin and your levels should have been ok by this point.
Could be that you are experiencing the dawn phenomenon, which means that you need more insulin for breakfast - more than you would have calculated for your insulin:carb ratio on the DAFNE course.
In answer to your question regarding HbA1c, then yes, spikes do cause damage to HbA1c readings. Unfortunately, persistent spikes like this will certainly adversely affect your HbA1c.