Well, you have been dealing with this for 30 times longer that me, so - firstly - I'm always in awe at the amount of perseverance it takes - and aware of how little experience I actually have.
(I should also state that I am very definitely not T1 - but I was diagnosed as one for a while, so only posting on that basis)
Secondly - I'm only close to one person who has a similar story, and he's been on a pump for the last year - and his HbA1c very recently was better than it has been in decades. Game-changer is not an overstatement.
He has been lowering his carbs as well though - I see it as going hand in hand, the better the control (via the pump) - the lower he can safely bring his carbs (and thus insulin) down, and the easier the control is, and so the better the control is... and so it goes in a virtuous cycle.
So - I'm just stumped at the attitude regarding denying you a pump.
I didn't know there was such a thing as hypo-unaware; so I've learned something...
Insulin resistance is fundamentally a state of elevated insulin while at the same time having it not work properly in tissues which have become "overloaded" for want of a better word - I realise that is stating the obvious, - has your dosing rate come down any? - 3.5 units/gm would really mean that the insulin is having to work hard - so that stacks up - and the answer is obvious; you have to get the insulin resistance down, it's only the equally obvious problem of how to do that safely.
Personally, I would be looking for another consultant - I don't see how a position of "nothing I can offer" is compatible with "I can't offer this".
I have some thoughts, but they get a little too close to diagnosing, which we just can't do... I would read up on Richard Bernstein - it seems to me that you are at the other end of what he referred to as "the law of small numbers" - ie, it's easier to control things with small adjustments - and thus much more difficult when things are swinging from one extreme to another.