I got v4.2.1 working on the Pi3!
Here is the steps I used. Some may or may not be necessary but it now works.
sudo apt-get update
sudo apt-get install dvb-tools
dpkg -i /location of saved deb file in the post above/tvheadend_4.2.1_armhf.deb
sudo apt-get update
sudo apt-get install libiconv
sudo apt-get install build-essential git pkg-config libssl-dev bzip2 wget
sudo apt-get install libavahi-client-dev zlib1g-dev libavcodec-dev libavutil-dev libavformat-dev libswscale-dev
sudo apt-get install build-essential git pkg-config libssl-dev bzip2 wget debhelper gettext libavahi-client-dev git-core liburiparser-dev cmake
the following steps resets TVHeadend to default if it was installed over a previous version. I found this was necessary.
sudo /etc/init.d/tvheadend stop
sudo rm -rf /home/hts/.hts/tvheadend/
sudo dpkg-reconfigure tvheadend
sudo /etc/init.d/tvheadend start
Thanks Lionel! Great work!