Hi Kristen,
Having many clients or companies on one instance of Moodle (multitenant support) is not a fully supported feature (https://tracker.moodle.org/browse/MDL-28946). You might want to take a look at the following threads:
https://moodle.org/mod/forum/discuss.php?d=205265
https://moodle.org/mod/forum/discuss.php?d=214071
https://moodle.org/mod/forum/discuss.php?d=111151
https://moodle.org/mod/forum/discuss.php?d=77915
The best solution, as you already mentioned, would be to have a Moode installation for each customer.