In addition to flying on less-busy days of the week, you can look for flights on aircraft that have relatively high numbers of Polaris seats. For instance, the ORD-LHR flights often use Boeing 767-300 planes, which have 46 Polaris seats (almost 1/3 of the total seats). The 777s and 787s have between 7 and 16 rows of Polaris seats, which can also affect the price & likelihood of upgrades. The ORD-MUC flights I checked next September use 787-8 planes, which have only seven rows of Polaris (28 Polaris vs. 209 Premium Plus & Economy)

https://seatguru.com/airlines/United...67-300ER_E.php
https://seatguru.com/airlines/United...ng_787-8_B.php

As always, a lot depends on the flight, the date, and the number of people competing for these seats. However, even as a 1K, I pay attention to the seat maps when I intend to use upgrades, and stay away from flights that have relatively few Polaris seats.

Good luck!