I saw no mention of what loudspeakers you intend or are using in the room. some speakers work well when others do not. Case in point, speakers with rear firing passive radiators will excite the room differently than simple front firing woofers or full range speakers. i don't pretend to know much but i do read. the Grado phones you are getting do have a better overall sound quality than the Sony phones you are using. To me, the Sonys are very bright and " in your face", practical to listen for molecular structure problems but not good for establishing a balance. The grados being headphones are also going to have the same basic problems if you intend to use them for reference or mixdown (too close to ears for accuracy sakes)
I have not heard the Grado 125 but i have heard the 80's and they shouldbe close to each other. We are talking about rooms and you are talking about headphones so a general idea of your speakers may help the experts here form a better opinion of what direction you may take. if you have posted about your speakers elsewhere, i apologize for not having read it, only this thread.
the experts warn against the use of phones for mixing. i admit it is totally a different world, headphone vs speaker mix.
I use some old jbls that belonged to a family member, some cheezy car door speakers in boxes someone built (alpine speakers) and an old sorry sony rack system someone was throwing away. based on this, my opinion is most likely bunk and unworthy but having read these things and remembered them, hopefully a few words i wrote could be of some form of help. my room has an old mattress leaning against the wall (covered with a sheet) and the room did improve quite a bit. it is behind me about 6 feet. i dont suggest you get a mattress.
One thing i do know, all of these systems sound different but good in their own way. i know if any one of them sound bad, something is wrong upstream and the mix or recording needs work. even the worst of
speakers should sound somewhat like a form of music.
ps, if someone has a keyboard (computer or otherwise) laying around they want to donate, i can provide an address (