I reuse the same configuration file for DisplayFusion across all my Windows machines, and I noticed:
The default function "Move Window to Next Monitor and Size Proportionally" can take one full second or so to finish its job when called upon locally using a hotkey;
In contrast, the same hotkey sends the window to the next monitor within a split of a second during RDP sessions.
Also, I observe window resizing/movement through AutoHotKey's default WinMove function also performs well enough locally (and its performance persists in RDP sessions).
Since it now takes a full second to move a window to the next monitor (and sending windows to the 3rd monitor to the right would take a good 3-4 seconds), another default function, "Move Window to Different Monitor (show monitor selector)", saves my life
However, this savior function, like other window-to-monitor functions, still performs rather slow locally (with a noticible lag, around 1 second or so).