• Version 41.65
• Singleplayer
• No mods
• Reproduction steps:
While first holding melee attack (left mouse button), and then also spamming the Push button (space bar), allows for reliably increasing the weapon swing speed to be the same as the Pushing speed.
Seems to work for any weapon regardless of how slow you would swing it normally due to various factors (fitness, weapon type, etc.). While spamming Push when swinging allows for matching the speed of the weapon swing to that of the Push speed. Of course, you still occasionally do an actual Push every once in awhile but for the most part the continuous weapon swinging at an increased rate is not all that difficult to maintain.