My problem was I had an outdated ppa file in sources.list.d. When I added the correct one, I was able to get through the installation, but cqrlog is not able to work with the old database. First, to recap what I did:

- Backed up ~/.config/cqrlog directory
- Removed the packages that were installed during the first attempt and re-installed the ones that were removed
- Installed cqrlog from the ppa
- Restored the backed-ip copy of cqrlog to ~/.config

When I start cqrlog it fails because of a missing database file (cqrlog_common). Here is the console output when I run cqrlog with --DEBUG=1. I've restored the database before with cqrlog and didn't have this problem.

mal@gumby:~/.config$ cqrlog --DEBUG=1

Cqrlog Ver:2.3.0 (001) Date:2018-06-17
**** DEBUG LEVEL 1 ****

SSL libraries:
/usr/lib/x86_64-linux-gnu/libssl.so.1.0.0
/usr/lib/x86_64-linux-gnu/libcrypto.so.1.0.0
Loading libmysqlclient: /usr/lib/x86_64-linux-gnu/libmysqlclient.so.20.3.12
**************************
MySQL version: 5.7
**************************
**********************************
MySQL version assigned: 5.7
**********************************
Loaded 89360 LoTW users
Loaded 95510 eQSL users
Loaded 46102 SCP calls
*
User home directory: /home/mal/
Program home directory: /home/mal/.config/cqrlog/
Data directory: /home/mal/.config/cqrlog/database/
Memebers directory: /home/mal/.config/cqrlog/members/
ZIP code directory: /usr/share/cqrlog/zipcodes/
Binary dir: /usr/bin/
Share dir: /usr/share/cqrlog/
TConnection to MySQL: 5.7
*
56 us states loaded
/usr/sbin/mysqld --defaults-file=/home/mal/.config/cqrlog/database/mysql.cnf --datadir=/home/mal/.config/cqrlog/database/ --socket=/home/mal/.config/cqrlog/database/sock --port=64000
2019-02-04 22:38:09 140714796715136 [Note] /usr/sbin/mysqld (mysqld 10.1.34-MariaDB-0ubuntu0.18.04.1) starting as process 22133 ...
select * from tables where table_schema = 'cqrlog_common'

CREATE DATABASE cqrlog_common DEFAULT CHARACTER SET = utf8 DEFAULT COLLATE = utf8_bin;

USE cqrlog_common;

CREATE TABLE bands (
id_bands INT AUTO_INCREMENT PRIMARY KEY,
band VARCHAR(10) DEFAULT '',
b_begin NUMERIC(10,4),
b_end NUMERIC(10,4),
cw NUMERIC(10,4),
rtty NUMERIC(10,4),
ssb NUMERIC(10,4),
rx_offset numeric(10,4) default 0,
tx_offset numeric(10,4) default 0
);
CREATE INDEX band ON bands(band);

CREATE TABLE dxclusters (
id_dxclusters INT AUTO_INCREMENT PRIMARY KEY,
description VARCHAR(100) DEFAULT '',
address VARCHAR(100) DEFAULT '',
port VARCHAR(10) DEFAULT '',
dxcuser VARCHAR(12) DEFAULT '',
dxcpass VARCHAR(20) DEFAULT ''
);
CREATE INDEX description ON dxclusters(description);

CREATE TABLE iota_list (
id_iota_list INT AUTO_INCREMENT PRIMARY KEY,
iota_nr VARCHAR(6) DEFAULT '',
island_name VARCHAR(250) DEFAULT '',
dxcc_ref VARCHAR(15) DEFAULT '',
pref VARCHAR(15) DEFAULT ''
);
CREATE INDEX iota_nr ON iota_list(iota_nr);
CREATE INDEX pref ON iota_list(pref);

CREATE TABLE dxcc_ref (
id_dxcc_ref INT AUTO_INCREMENT PRIMARY KEY,
pref VARCHAR(20) NOT NULL,
name VARCHAR(100) NOT NULL,
cont VARCHAR(6) NOT NULL,
utc VARCHAR(12)NOT NULL,
lat VARCHAR(10) NOT NULL,
longit VARCHAR(10) NOT NULL,
itu VARCHAR(20) NOT NULL,
waz VARCHAR(20) NOT NULL,
adif SMALLINT NOT NULL DEFAULT 0,
deleted SMALLINT NOT NULL DEFAULT 0
);
CREATE INDEX pref ON dxcc_ref(pref);
CREATE INDEX adif ON dxcc_ref(adif);

CREATE TABLE qslmgr (
id_qslmgr INT AUTO_INCREMENT PRIMARY KEY,
callsign VARCHAR(20),
qsl_via VARCHAR(20),
fromdate DATE
);
CREATE INDEX callsign ON qslmgr(callsign);
CREATE INDEX fromdate ON qslmgr(fromdate);

CREATE TABLE log_list (
id_log_list INT AUTO_INCREMENT PRIMARY KEY,
log_nr SMALLINT NOT NULL,
log_name VARCHAR(50) DEFAULT '',
auto_open SMALLINT NOT NULL DEFAULT 0
);
CREATE INDEX log_nr ON log_list(log_nr);

CREATE TABLE db_version
(
nr SMALLINT NOT NULL
);

TApplication.HandleException TMySQL57Connection : Error executing query: Can't create database 'cqrlog_common' (errno: 2 "No such file or directory")
Stack trace:
$000000000091B09F
$000000000091C788
$00000000006CA63A
$00000000006CAE83
$00000000005AE435
$000000000080E3E9
$0000000000740123
$00007FBFDB836C73
Closing DXCluster window
Closing TRXControl window
Closing GrayLine window
Closing dDXCC
Closing dData
Closing ini file ...