Do you mean glycine? I've not heard of glycerine having a positive effect on sleep, although glycine is often recommended.
Glycine is an amino, glycerin is a triol.
When I tried to search specifically for "glycerin" and sleep I just get a couple of reddit threads, but no real sources.
A cursory search shows lots of redditors taking Vitamin D (some of them way, way too much btw) and having wild dreams too.
I take 800IU a day and haven't noticed anything on that little.
Yes, I wouldn't expect to notice anything on my dose.
When I took >5000 IU daily for three months, I only raised 25(OH) D level in my blood from 9 to 30 ng/ml, and there's no evidence of toxicity below 150 ng/ml.
Of course, when dealing with high doses you need to keep your levels in check, as absorption can differ between individuals.
Your 4000IU isn't too much. Lots of the brands you see in stores are 5k for daily supplementation.
By what metric? Jeez. People, you need to get your blood checked. There is no one-fits-all dosage. In winter, 4000 IU/d was enough to raise my blood levels well into the excessive range.
I fully agree that supplementation should always be combined with both blood testing and also a general medical evaluation.