@jacksimmons I haven't had a chance to listen to your recording but from what you have described a few things spring to mind...
The makn difference between listening on speakers v headphones is the effect that the room has
Talking about it is one thing - but I think you should do a little experiment to prove what is going on
Without changing anything with your setup play the logarithmic version of this full frequency sine sweep
https://www.audiocheck.net/testtones_sinesweep20-20k.php a perfect situation all frequencies will be heard equally so the volume of the file should be consistent
Your ear is likely to favour some frequencies BUT I think you will notice some very dramatic peaks and dips in volume at different frequencies (and if you play the file through a graphic eq that gives you a visual representation of the frequencies you will be able to identify where your room is emphasising or cancelling certain frequencies)
I suspect your room dimensions are causing standing waves
A cheap solution to get a more accurate response is to check your speaker placement (I would suspect they are too close to the wall)
You could also consider some type of isolation material between your speakers and desk/stands
You can then start to consider some acoustic treatment for your room to deal with key reflection points
Here is a great little guide , and be sure to check out the box about room dimensions and standing Waves
Headphones are often frowned upon for mixing - but one does have to wonder if it is better to mix on headphones than in an untreated room which is causing issues
I personally like to use headphones with a VRM box, which mimics the experience of mixing on speakers. This is now discontinued but Waves and Sonarworks have similar software based products
Finally, don't forget your end listeners will not be in treated rooms with perfect monitor speakers
Your mixing is therefore more about getting the song to sound good on different systems- so as
@tone has rightly said the more you "learn" your mixing equipment & environment the more likely you are to make the right decisions when mixing