Hey CB- hope things are going better for you, maybe even better than you expected they would be going at this point in time. I may have a little insight for you, based on my personal battle with CH, and I noticed no response to your question, so...
23-Yr Vet with CH here...no meds other than non-RX stuff that, if it worked at all in pain-reduction (sometimes killed CH in a few minutes if taken promptly) was only good for a few years, and I use little if anything for the past 10 years, it seems. I used to get hit with 3-4 month cycles, 3 CH/day, sometimes 4, 3-4 hr duration, 6-7 days/wk, remissions were sometimes shorter than cycles (2-3 cycles/yr, have had 4)...sometimes I was basically borderline chronic CH. Seems I'm heading into some sort of long-term remission from the beast since 2008 on the 18th year, as everything to do with CH has slacked off, with longer remissions, shorter cycles, shorter CH (about 1/4, but sometimes a few hours), less CH cts/day, usually. I'm still coping, and in the middle of a cycle as I type, but CH has been sporadic the last 24-36 hrs...I may be nearing the end of this cycle after about 8, maybe 10 days...I'll take that over 4 months, no problem...I sorta lost track of this round already...all in all though, lucky me to be on the down-hill side of the slope!!!
Your mention of a cold can on the head (never tried that, so, thanks for another possible weapon to fight with...

, then asking about brain-freeze from ice-cream reminded me of what I just did a few nights ago, that I do frequently with night visits with the beast, which is to step outside and breath the dense, cold night air (higher O2 concentration and chilling effect)...in through the nose, out the mouth, DEEP, slow breaths at first, then pick up the pace as needed until the effects begin kicking in (just don't hyperventilate with cold air...hurts my lungs after a minute or two)...it cools the sinus cavity and seems to take the edge off for most of my night CH when massage/pressure-points fail...the colder the air, the more effect it seems to have...works pretty quickly for me in mid-winter when it's -20 to -30*F outside. Night before last it was about 25*F and snowing with high humidity (wet snow), and I felt relief coming within about 2-3 minutes...I slowed my breathing to about 20/min and gave it another 5-6 minutes and went inside...maybe another 10 minutes and I was back in bed...still a bit uncomfortable, but dropped from about 7 Kip-Scale to 2 or less...slept soundly soon after. Back in the day when I was hammering it out in the 9-10 Kip with 2/3 or more of my daily CH, this method would reduce the beast to maybe 4...won't subdue it entirely, but the reduction in pain is significant enough that I use it whenever all else fails...has always worked for me in CH pain-reduction, and for over 20 years now. If you're in a climate/season where nights aren't cool/cold, this won't help much...my summer CH weren't effected if it was a hot night....cold, dense air seems to be the key.
That said, you may be onto something with the brain-freeze, although you may not want to take it to the point of hitting that painful stage where it makes you groan in agony...suggest just a few good-sized spoons full to start, let the cold soak in for a few minutes, then hit it again, just to the point where you notice your CH pain changing, then it may begin to reduce it shortly after. Hopefully it doesn't supercharge the CH and make it worse, but if an external cold source helps the pain, the ice-cream might do even more if regulated correctly for your tolerances. Thing is, you may find that a all-out brain-freeze causes a distraction form CH, enough so that you don't notice it for a period of time...either way it may help.
Give it a shot and see what happens...let us know...I'm curious if it might work, myself.
You're definitely not alone...just found this site a few nights ago, myself...lots to read, but I'm going to get on the vitamin D-3 preventive regime shortly...sounds very promising, and far better for me than injections or oral drugs.
Wishing you, and all of us, PF days & nights.