Hi there,
Sorry if my tone sounds rushed but I'm in the middle of packing to move house next week. My cat, Saoirse, was initially treated with Caninsulin and we had similar issues to you. It was a difficult time and I hope some of our experiences might help you avoid some of the pitfalls we encountered.
1. From what I've read here, ketones can be a risk even when a cat is on insulin and even at lower BG levels. Testing with urinalysis strips is straightforward and will help keep Ashley safe. (Saoirse's not ketone-prone but I still checked her anyway.)
2. Caninsulin is a very harsh insulin. As you've already seen it can drop the BG level hard and fast. As already mentioned above, food must be eaten at injection time. Saoirse was miserable and poleaxed on Caninsulin for 9-10 hours out of every cycle. She used to hide most of the time and tried to avoid being injected. Her mood and demeanour is much better on Lantus, and while injections don't fill her with joy, she doesn't run to hide any more. In general, Caninsulin is not a great insulin for cats. Insulins such as Lantus and Levemir are gentler and longer acting (might be worth considering going forward - you can learn a lot about different insulins here). Let your vet know about Ashley's mood, appetite, energy levels and behaviour as well as BG numbers.
3. If you are getting big drops like that, based on my experience I would recommend that you test early in the cycle so you can catch big drops in numbers. After insulin, if Ashley starts looking for food - even if she doesn't eat any - that can be a good indicator that the Caninsulin has started to kick in. Close monitoring of clinical signs and BG in the first 3-5 hours - is a great way to keep your kitty safe. I usually tested at +2 or +3 to see how hard and fast the drop was going to be. If I saw a strong appetite uptick I would test immediately. If a drop was sharp, I tested again shortly afterwards and checked again until Saoirse was past nadir (lowest BG in cycle). This is especially important in the early days when you don't have much test data and don't yet know your kitty's pattern of response to the insulin. I am fortunately in the position where I can monitor throughout the day but if that's not possible, the +2 test can be very valuable as an early warning indicator that closer monitoring may be needed.
4. I've only been on this board for a few months but I have seen a number of cats here that seem to have digestive upsets and appetite changes when they start insulin treatment. Of course, some are to be expected. If your cat has been polyphagic (constantly hungry despite eating more, and possibly losing weight at the same time) then insulin will help her to start using her food better, thus reducing her need for extra. However , I have seen several cats here exhibit nausea symptoms and these can lead to inappetence. (Saoirse has pancreatitis but I think some of her early nausea and inappetence problems were insulin-related based on my observations of her. I've also seen anecdotal reports of human diabetics experiencing tummy upsets from insulin. You can find a really good guide to nausea symptoms plus both natural and medical remedies for same at the link below:
Tanya's Site - Nausea and Appetite Problems
I tried all the tricks listed above for Saoirse with limited success. I eventually got the right meds for her (famotidine for acid stomach, ondansetron for nausea, cyproheptadine for appetite) and things got much better for us. In my endeavours to encourage Saoirse to eat I ended up triggering a pancreatitis flare. Granted, our situation was complicated by Saoirse's then low-grade pancreatitis but if I adopted another diabetic cat in the morning and she started showing signs of nausea I would try the temptation techniques for only a short time before going to the vet to get help, doubly so where Caninsulin is in the mix because of the precipitous drops that are its hallmark - for both our sakes. (Appetite problems are tough on both cat and caregiver: earlier intervention would have saved the two of us an awful lot of distress.) If it's just a tum upset, a short course of famotidine and/or an anti-nausea med might be all the meds needed until the body adjusts to the foreign insuiin. Definitely let your vet know about the problems and ask for lots of advice about dosage.
Hope some of the above helps. Sorry it's so rushed (and not proof-read

).