If you want to use EQ correction, why not EQ-correct your monitoring (the opposite way you would your master), instead of your master ?
Personally I would reserve that solution for extreme cases, however (like when I mixed student films for optical 16mm - the loss of HF was so drastic, I just couldn't compensate by ear), partly because it's approximative.
Other alternatives are: get used to your BD770's sound (by listening to a bunch of other music you like in it)... and if you can't get used to it, then replace it.
Just as it is a good idea to check your work on other systems, it is also a good idea to listen to works of the quality you aspire to on your own system, to get a reference. As others have suggested in this thread.
As for replacement... I don't know your budget, but the Senheiser HD25 is a reliable headphones set, a de-facto standard, and still affordable enough. Or save a little bit for decent monitors. Here's a thread about affordable ones:
https://vi-control.net/community/threads/best-studio-monitors-for-price-quality.79727/ - but before you open your wallet, know this: if your room is small and rectangular (or even worse, a square), new monitors won't help you much in the bass department - not without serious acoustic treatment.
The thing to remember is that what's in the center will get a slight boost in mono.
Since mono sounds more crowded than stereo, compensate for it by placing what needs to stand out in the center. That's usually the soloist or vocals. And the percussions, if you make percussive music.
We also like to place the bass in the center, but for another reason: since the human ear can't locate low frequencies well anyway, this reduces the risk of clipping one channel, by spreading the high energy of the bass equally across both channels.
I know this is more than you asked for, but it's free