Database design for monthly leaderboards
After thinking around a bit more, a solution I think could work would be to have a new table of monthlyScores, structured like this:

+----+--------------+----------+--------+
| ID |  userID (FK) |   month  |  score |
+----+--------------+----------+--------+
|  1 |            1 |  03/2019 |     12 |
|  2 |            1 |  04/2019 |     23 |
|  3 |            2 |  03/2019 |      3 |
|  4 |            1 |  05/2019 |     22 |
|  5 |            2 |  06/2019 |     11 |
+----+--------------+----------+--------+


Where month is the current month, I could increment this value for the current months' games, thus meaning I could provide a leaderboard of the leaders for the current month. Similarly I could display scores for each user for previous months.

Posting this here as an answer as I feel like it could work. That said, as you can probably gather I'm very new to databases and so would be interested to hear about other solutions, and/or if this is advisable!