I ended up offering my cat a high-carb treat in the beginning. I'd give him one piece of Meow Mix Tender Centers as a reward. I agree it's not the best choice, but literally 1 piece for cooperation wasn't going to do much to his blood sugar. Once cooperation was ensured, I moved on to low-carb treats.
A small amount of WHATEVER he goes bananas for is ok! The reward doesn't need to be a treat either. Anything he loves can be a reward: petting, brushing, playing, etc.
My cat Peanut sounds so much like your cat. He's not big on being touched, and unfortunately he is not very food-motivated anymore. His greatest love is the outdoors. I often reward him by opening the window for 2 minutes regardless of the weather so he can smell the outdoors.
I am really surprised that China mentioned singing because Peanut loves it when I sing. He specifically likes the Ponyo song where I say "Peanut" instead of "Ponyo." No, I don't sing well, but he still enjoys it.
Lantus is dosed based on the nadir reading, which usually (but not always) occurs at +6. You do need to test before you shoot, but getting that nadir is going to be important too. I don't feel comfortable making dosing recommendations without more readings. I'm sorry.

You're probably going to want to follow the Start Low, Go Slow method.
Training him to come to a designated spot should help. I suggest continue the forcible testing as you always have and introduce the training separately. The training can go in steps: (1) train him to come to the spot, (2) add ear-touching, (3) add clicking the lancing device--without touching him with the lancing device, (4) do not have a lancet in the lancing device and click it while holding it against his ear as if you were actually testing, (5) start testing for real.
Peanut is still a sensitive cat, but he was incredibly more standoffish and skittish when he first came to us. I made some adjustments to our home and interactions with him based on Jackson Galaxy's show and books, but he also benefited from anxiety medicine.