Oh, sorry! I hate to tell you... I'm 23 weeks and have had this problem from the beginning too. Just like you, I hit the pillow and fall asleep RIGHT away, then anywhere from 1:30 to 3, I'm awake until about 5, then my dd wakes up about 5:20. So much for that! Frankly, I'm sick of it. I only had it in the third trimester last time as well. I've tried just about everything. I hope you fare better than I have. I don't fare well on the 3 to 5 hours a nignt I'm getting. I'm an 8-9 hour kinda gal.
If you find a solution, share it! Please! Until then, I offer no advice, only empathy.