Insulin resistance?

How long before eating do you prebolus? Going high after eating suggests you digest carbs faster than the Fiasp starts working.

Regarding morning corrections, have you tried eating a small amount? Dawn Phenomenon happens because your liver is dumping glucose. If you eat something, your liver may get the message that it doesn’t need to dump as much. Some people find this helps even if it just something small like a yoghurt or a few berries.

I think it is worth exploring the hypothesis that you are double diabetic given the persistent high blood sugars in spite of your insulin doses.
Before you did that I guess a nurse might ask if you've got any lumps where you inject that migh be causing the insulin not to get through? If so you'd expect some unpredictability with bgs not doing what's expected or what's worked before.
Do you have any other indicators of insulin resistance e.g. weight gain, higher triglycerides than hdl , high blood pressure?
If you did a day of not eating any carbs or protein (the nutrients which will raise your blood sugar) what would your levels look like on the current basal dose?
I had a high hba1c recently and was reluctant to increase my basal but have done so and my average bgs are down so you may just have to bite the bullet there. It may be needed because I am 50 and although I'd hate to admit it, my hormones may be causing more resistance. Not sure if its been mentioned but splitting tbe hasal can be helpful as they don't always perform by what it says on the proverbial tin.
If you've got your basal correct it does become a lot easier to do bolus dosing IMO because you aren't always chasing your tail with correction doses.
I am sorry that your DSN is using a stick rather than a carrot re the FSL and I think the only way to counter this is to prove her wrong by using the libre to adjust your basal rates. Ideally keep asking for a pump because that's a great tool to counter stuff like the Dawn Phenomenom.
If you are in any way insulin resistant then going low carb will help. You keep your basal rate but obviously adjust boluses erring on the side of caution! I find I need half the dose in a protein based meal as I did for a carby one but it might be wise to try a third of the dose and NOT go on a long walk afterwards!
The exercise part of this involves doing a little more work to get strong muscles (squats,lunges, push ups, hill walks rather than strolls) t o make your body more sensitive to the insulin you're injecting.
If you start out with a high bg but not enough insulin your blood sugar won't come down and may even increase because your liver will pump out more glucose in response to the muscular demands i.e. walking isn't a solution for type 1s to reduce blood sugars unless your blood sugars are under 10 in the first place.
Anyway that;s my 2 ps worth - hope you feel better and more in control soon as I know how I feel with higher blood sugars and the feeling that it is my 'fault' and it's not great!

Did you have your Coronavirus Vacinne recently? I'm also on Tresiba and Fiasp and found I had to both take more insulin and give it longer pre-boluses. It's only starting to come back to normal now, with the Fiasp getting faster and better at dealing with Carbs.

Understand your issues.

Clearly the DN thinks you are not carb counting correctly and sounds like she does not belive the patient is telling the truth which is a hard thing to take when you are telling the truth. I also understand a body can have very different requirements over a course of the day and night so having a steady level over the night does not mean a steady level during the day and this is when a pump will really help and realy think as suggested you need to keep asking for a pump.

When I did a 24 hour basal test (didn't have a CGM so yes woke up every hour to test during the night) I got the strangest grapgh you have very seen, an n shape over the 24 hrs nothing like the flat steady grapgh the manufacturer suggests. Basically a rise in the morning (likley DP) then a slow drop from 2pm till lower levels to late evening. On the consultant review - here have a CGM! and nothing else.

Since then (during 2020) I have got a change of insulin (Basal was Lantus now Tresiba Bolus Humalog to FiAsp but you are also on these as well) I have stop using Libre for my own reason. But I still have strange result that don't make sense.

I need to do another Basal test with the new insulin I have and I am also considering eating the same for a week and hopefully (in a strange way) I continue to get the strange result as I also have the issue with the consultant not believing the patient.

Hopefully when you have your next concersation with the DN they will believe you.

All the best