Thoughts/experience
Was on Remeron 7.5mg for several years to help me get back to sleep after having to get up for pain and bathroom issues. My colon was removed entirely due to colon cancer so I visit the toilet about 9 times/day and usually 3 times overnight.

But yes, it resulted in drowsiness/grogginess and almost hangover-like side effects - not just in the morning either. It did not get better with time for me.

After retuning/adjusting my CPAP machine so it became much more effective, I weaned off of the Remeron gradually over a month-long period to see if it was still needed and found that it no longer helped the night interruptions. I have since noticed an improvement in the morning drowsiness/grogginess and the feeling tired throughout the day. It's only been a week off of it entirely, so this may improve more.

That does make sense because Remeron's half-life is 20-40 hours and can stay in the body for up to 8 days. Net - this carryover that you and I experienced does happen.

It's unknown what half the previous dose will do - you certainly can try it and stop if the side effects are unacceptable.

Good luck.