@AnnS do you know if your levels continuously rise throughout the night or start to rise in the early hour?
The reason I ask is "Dawn Phenomenon" - our livers helpfully dump glucose into our blood to give us energy to start the day.
If this is the reason for your high waking level, increasing your basal insulin will be less helpful - you are more likely to hypo before the liver dump.
Unfortunately, the only way to tell is to set an alarm at around 2 or 3 o'clock to check your levels ... unless you have a CGM or Libre
It could be worthwhile applying for the Libre trial of you don't have one. Checkout their website, if I remember correctly, the free trial is pretty obvious.
With regards to your Fiasp timing, when you say you "spike slot" does your level return to normal levels after the spike? And how high do you spike?
Even people without diabetes will spike when they eat. Depending upon the meal, they can spike to around 9mmil/l. If this is what you are are seeing, I would not stress. Our levels are not supposed to be flat all the time.