I won’t say that I’ve had as severe an issue as you with the hot pillows (ie: no head/neck sweating), but I’m one of those people who if I happen to wake up in the middle of the night, I need to flip the pillow over, or roll over to find a cool spot on the pillow, or even sometimes grab the “backup” pillow to feel cool and get back to sleep. I can’t just close my eyes in the same spot and drift back to sleep. Once I get hot, I tend to stay hot, and getting back to sleep becomes a pain… I came this close to buying a shredded latex pillow which had great reviews and allegedly slept very cool…
That said, I was walking through Bed Bath and Beyond a month or so ago and came across a “Comfort Revolution Hydraluxe” pillow. It’s all memory foam, with a layer of gel bubbles laminated to one side. I’ve since seen similar pillows with waves of gel instead of bubbles, and other similar versions from other brands. This one was out on display with a tag saying to push your hand into the pillow and count out 20 seconds, so I thought “sure, I’ll give it a shot”. About 10 seconds after pushing my hand down onto the pillow the thing felt SO COOL like it was just sucking all the heat out of my hand! It wasn’t exactly “cold”, like an ice pack or anything, but it was so different from any other pillow I’d experienced in how cool it felt. I was essentially sold immediately, and went online to find the cheapest deal I could on a king-size version 
I’ve been using the new pillow now for about 3 weeks, and I love it. Every night I put my head down on it, it sucks away all the heat making me feel very cool, and I fall right asleep. Online reviews tended to say that the cooling sensation from the gel layer only lasts 15-20 minutes, and if you don’t fall asleep within that time its not any cooler than a regular memory foam pillow, but in my case it’s been great. On the off chance that I do wake up in the middle of the night, the king size pillow is so large (I’ve only ever had standard pillows before) that there’s a whole 50%+ of cold gel waiting to suck the heat out of me all over again
NO problems at all getting back to sleep so far.
In the interest of full disclosure I’ll share the two minor negatives that I’ve noticed about the pillow. First, the thing had a strong chemical smell that I could still detect after 2 weeks or so. This really surprised me because we just got a new Novosbed (memory foam), which in my opinion had only a very faint odor and only if you put your head right down on it, even from the first moment we opened the plastic bag. After a day or two any odor in the mattress had completely dissipated, as far as my wife and I could tell. This darn pillow though was far stronger smelling than the bed ever was, and the smell has only just recently seemed to go away in my 3rd week or so of using it. I’m fortunately not sensitive to the odor, but if you are you’d use up most of a retail store’s 30-day return policy just letting the thing air out to the point you could sleep on it 
Second minor complaint, this particular pillow is very thick, around 6" I believe. I can barely fit my pillow case around it, it’s practically busting the seams! The king size pillow weighs 10 lbs! (literally, not an exaggeration at all). I’m mostly a stomach sleeper, and while I prefer a thicker pillow than I suspect is normal for stomach sleeping (my old standard size down pillows I used to fold in half to bulk them up…) this is right on the edge of being too thick for me. My first couple nights it felt very strange to have such a thick and supportive/firm pillow, but now after several weeks I believe I’m getting used to it. I loved the cooling sensation so much that I really just wanted it to work out as long as it didn’t cause me pain or otherwise affect my sleep, which so far it hasn’t… For back or especially side sleeping, the thickness would be less of a concern, but just pointing it out.
In any case, you may want to look at something similar, as I said there are a dozen brands out there with similar gel-laminated foam pillows, even the Tempurpedic’s and other pricey brands have versions of the same idea. For me, it was exactly what I needed, and never knew to look for.