NO, you should not use the regular 17.1 EGroupware, but the *-compat Archive and add that to your already installed 19.1. Remove all tables in the database and restore the 1.6 ones from backup and then start the schema update again via setup. It should be unpacked in the EGroupware installation directory, so you have an additional phpgwapi directory (the others don’t matter, nor harm). After successful update to 19.1, you can delete the extra directories again.
No, instead of updating the database, you can also use your 19.1 install to take a backup to install in our hosting or on a virtual server, as I suggested before.