Any lancet that is 26 gauge or so in size will work. You can use the ones for Human diabetics. Any pharmacy sells them or look online. Buy the matching device if you prefer.
How long to hold the warm rice sock on the ear depends on how warm the sock is and your cat's ear. Try at least 30 seconds before poking. Hold the sock under the ear so you have a firm surface to poke against. If there's no blood, warm the ear up longer. If the sock isn't warm enough, rewarm it for a second or two longer next time.
Is the Libre meter not an option?
There are meters that test for both blood glucose and ketones but the test strips are really pricey. If you just can't get urine for testing, then buy a combo meter.
Have patience

Those high numbers are frustrating to see but your cat is on insulin and the right diet. You just haven't found the right insulin dose yet. Dose increases are made slowly.
You can ignore the vet's advice about everything food related (when to feed, how many meals daily, what to feed, etc). Do not ever feel bad for agreeing to disagree with the vet. You know what's best for your cat. You've said that your vet isn't experienced with diabetes. Just use the vet for check ups and vaccinations and prescriptions. Take the advice of FDMB members for insulin dosing and share the spreadsheet with the vet. If you need to get a new vet, don't feel guilty about hurting the vet's feelings or anything.