What about gluconeogenesis on LCHF?

My body I converts protein rapidly. It is also said that in the absence of carbs gluconeogenisis will proceed rapidly.
I don't understand your chicken calculation though. 1 oz of chicken is about 8 grams of pure protein after its cooked. A little higher if it's all white meat. There is 28.3 grams in an ounce.
Did you check at 2 or three hours as protein CAN take that long to peak.
I'm curious how you would get your complete protein if you went vegan? I would assume beans and rice are out.
I find I tolerate a bit more protein at lunch and dinner and very little at BF. I eat 1/2 an avocado and celery for BF and save small amounts of protein for lunch and dinner

If you just started reducing your protein and / or carbs it could take a while to empty your glycogen stores and adjust. I need to be in ketosis at all times and have my glycogen stores depleted regularity. Having a vegetarian breakfast helps. It is difficult finding the right balance. The only only thing that works for me is VLC ( 5%)small amounts of protein (15%) and 80% fat. Also keeping meals very small. Even a small handful of green beans and broccoli raise me. My meals look small but they are satisfying. I put an ounce or two of protein and fat on a lettuce wrap and have more guac with celery and a radish for lunch and dinner. I have found guac to be magical as it slows the ups and really slows the lows. Also keeping meals small keep me lower. And as a RH I would imagine that would help you too and having a few nuts or nut butters in between as well. I hesitate to say cheese because I have read many times dairy is very insulinogenic and it certainly raises me and requires additional insulin.

Fat and protein slow things but they don't stop them as you know. I think slower is better of course.

I have thought of vegetarian but have no idea how I would get complete protein. Protein powder is known to cause spikes. I eat 30 g animal protein and get a little additional with nuts and pumpkin seeds as well as avocado and veggies so I estimate about 35-40 total and that is rosedales recommendation for me. Weight went down initially but has stayed steady for quite some time. I watch my muscles as well.

Perhaps test the chicken again in a proper meal, with veg, and butter (or oil of choice) on the veg.

And certainly don't dismiss chicken without repeating the test. There are several possible explanations for bg rising by 1mmol/l that don't involve chicken, including stress, physical activity, laughing at a tv show, being tired... Test the chicken several times before making any assumptions.

We had a lady talking about how a cup of coffee raised her bg from 6 to 12 mmol/l. She was understandably shocked. She repeated the test several days, and it never happened again. Imagine her relief to realise that coffee was still back on the menu!

I hope it didn't sound like I was implying to ditch the chicken. I love my proteins, I just have to moderate them.
But I am type 1 and very different from RH so much testing is needed.
I do find it curious how protein effects everyone differently. I loved my high protein days. Chicken dipped in the mayo was heaven. Still do it but much less protein but I am also much older now and not nearly as active.

I think you are finding, little and often more preferable, than the bigger meals, and you can use protein as in meat as a basis in most of them.
Utilising vegan will give you more options as well.
Unfortunately it is a huge pain in the !#/?, buy once you find out what you can live with, and you stay in the normal range, your body will respond in kind.
It looks as though your hypo awareness is very good and you can use that while experimenting, especially if you overeat or try something new.
Test, experiment, test, experiment, test!
I have every faith you will get there.

Hope your family troubles sort themselves out!
Best wishes.