Sounds like both your headphones and monitoring are going to be difficult to yield good translation.
Sounds like both would need to improve to get to a point of not having to remix and remix again.
Certainly as mentioned, you should get monitors but .... getting real monitors is not an easy task, in the sense that you will pay for them (at whatever level u can afford) and then you will pay 5 to10 times that to treat your room close to properly. It is something to work towards.
In the immediate sense some better headphones would help before spending the $ to getting real monitors eventually.
I don't mix with headphones but do use them as a reference. I have Beyerdynamic DT770 an 880, AKG 240 and 701s, and the pair i actually use the most as a mix reference are my Yamaha HS10, I think that is the model. They are the headphone equivalent of the NS10 monitors. They are direct and focussed much like the NS10 and I feel of what I own they are the most accurate reflection of the mix and while not being made anymore? I think, they were around 100$. I think after about 1 hour you will have some fatigue mixing with them , but that is what you will get with most headphones.
I ask have audeaze a nice set of audiophile headphones and wouldn't mix with them, but they sound great for listening all day but not cheap.
Oh yeah another factor is the impedance, as my AKG an Beyers sound nice too, but sound best with a nice headphone amp, which is more $, while the Yamaha's are extremely responsive even at iPod, iPad levels. Certainly for plugging into a synth or something the Yamaha are best, the others do not go loud enough at max volume on for example our NORD Stage piano. SO these are versatile which might of value to you.
I would start there until I could get a monitoring system going.
All the best to you and your music!