I read this as not 'stacking'. You can HAVE Reaction Enhancers AND Improved Reflexes. You'll take the higher of the two in each place.
Reaction Enhancers 3 and Improved Reflexes 1 will give you +3 Reaction +1d6 Initiative. It's a horrible way to go about doing things, of course.
The only time you can stack Reaction Bonuses is when using Reaction Enhancers and Wired Reflexes in Wireless Mode.
The only time, as far as I can tell, that you can stack Initiative Dice is the Increase Reflexes Spell and Drugs, these being the only two sources of Initiative Dice increases that don't specifically mention that they won't combine.
Based on your House interpretation, Wired Reflexes won't combine with any other Augmentation, so your GM might rule that it can stack with the Increase Reflexes spell or Drugs.
For Missions play, I believe Bull has ruled that ALL increases are 'augmentations' whether they are called that in the book or not (so from Spells, Ware, and Drugs) so you cannot combine any Initiative sources.