I realize this is 4 years late-er. However, in an effort to help others I'd to post my experience.
I've been a diabetic for 40 years and I too get hiccups when my BG spikes but only at night. My only relief is sitting up in bed.
I have also noticed a considerable amount of thick saliva building up in my mouth, which shows a relation to the hiccups as my throat may be closing to keep it from my lungs while sleeping.
I do not have this happen often and it hasn't always happened. It began close to 20 years with the disease. I feel for anyone else who experiences this and the only recommendation I can give is to practice better control of the BG. We feel so much better when we do and in my case, I can usually pinpoint the problem (i.e. something I ate that wasn't a dietary recommendation). I do not always pay such a price but there's nothing to blame for that one but I, eh?
The systems always subside but sometimes not without coverage insulin. Usually 4-6 iunits of regular or wait it out until the longterm dose catches up.
Somewhat off topic but for those who've tried fruit to satisfy that late night snack or urge to eat something sweet, I've had fantastic success with this. So much that I've switched to fresh cut fruit for all snacks. Something about the fruits sugar that is more tolerant and easier for my body to process. I have definitely felt a big difference when eliminating ALL processed sugars from my diet along with more stable A1C's.