Hi Jamie
Welcome to the forum.
It's a difficult dilemma to be in - my best advice if you want to win over the DSN's and Consultants is to be the best t1 you can be, when they can see that you are already working at this to get the best results then they will support you, using any form of technology is pointless unless you can make it work for you otherwise you are driving a formula 1 car in first gear and not getting the full potential so the cost of funding for a libre is pointless unless you know how to achieve the best results from it, which is why they are reluctant to fund it, and unfortunately using any technology is not a magic wand to good control either, it's down to you to master it and know what you want to achieve from it.
In regards to your current situation, have you done the Dose Adjustment for Normal Eating course yet ? if not get your DSN to sign you up to the next available course, having done DAFNE is a pre-requisite to become considered for a pump. Get knowledgable and read up, a great read for type 1's is 'Think like a pancreas' written by a type 1.
It's vital you start to test more regularly, testing tells us many things, it's tracking our control, telling us if our bolus ratio worked, if we need to correct. By taking ownership of your control means your team can see you are working hard at this and will support you more. Also a query - why are you taking insulin after meals ? quick acting insulin should always be taken before you eat, some pre-bolus by up to 20 mins to avoid the spike.
I self fund the Dexcom G6, I don't get funding for the libre, I do have the pump but had to push for this for over a year to get access, it was on the basis I was testing regularly had done DAFNE and was still struggling, they could see I was working incredibly hard already and was refused also but didn't give in, since using the pump i've dropped my HbA1c and dropped it even further with the G6 but because I am aggressive with correcting highs and managing my bolus and basal ratios very carefully too, I do put in alot of work each day to keep control still now though, it's not a walk in the park but it's easier because i've gained the knowledge to be the expert at this.