I'm not sure how to define "speed hiking". Is it hiking fast or hiking a long distance in a day so you complete a section in fewer days then "usual"? Since it's coupled with trail running, I suspect it's hiking at a fast pace, but not quite running.
Depending on how long a drive it is from your friends place to the trail head, you'll probably loose an hour on each end coming and going. Maybe another hour between getting up in the morning and getting on the road. So add at least 3 hours to your 16 hours of hiking. That's 19 hours out of 24. That doesn't leave much time for sleeping. So, basically you won't get any between day 2 and 3.
Lets say you get up at 4 AM to be at the trail head by 6 AM. 16 hours later you finish, so now it's 10 PM (you will be hiking in the dark). Another hour to get back to your friends place, assuming your friend is there waiting for you to show up. Now it's 11 PM. You still haven't had any dinner. You finally get to bed at midnight and have to get up again at 4 to do the next day.
Day 3 is a little shorter and a little easier then day 2, so maybe you can sleep in a little, but not by much. You'll be sore, sleep deprived and possibly nursing some blisters on day 3, so that hike could take longer then expected. I hope your not planning on driving home right after that.
Carrying enough gear so that you can comfortably spend the night on the trail will be a good idea. There are few bail out points in that section. Cell coverage could be sketchy too. Since you'll have enough to spend the night on the trail, you should just do that between day 2 and 3. That saves time and is less of a burden on your friends picking you up late at night and then trying to get you back on the trail early the next morning.
You'll have a better idea after day 1 if you should attempt day 2 or not.