Asalam alaikum brother,
A few weeks ago prior to Ramadhan a local scholar came to our mosque,alhumdulilah, and gave a khutbah on something similar to this. I'll try to help you with your situation with his guidance. To more or less of the effect he said there can be 3 possible recommendations that a person can do for undoing the sin involved in being negligent toward obligatory prayers in the pasttime of his lifetime.
The first recommendation,to more or less of the effect was that a person must offer all of the lost prayers as soon as he realizes their importance and significance that he hasn't made in the past. A possible method that ifyou allow me I may suggest is to offer each of the five daily prayers twice (only the fardhrakahs that is), once to fulfill the present prayers and the second time as a recompensation for one of the lost prayers of the past...
The second recommendation he gave was that a person should regularly offer his present obligatory prayers and then after them he should attempt to try to offer as many supererogatory (nafil) rakahs as may be possible for him during the time and pray that Allah shall accept our supererogatory rakahs and shall accept them as a recompensation for our previous missed prayers of the past,insha'Allaah.
The final recommendation as I recall it was that the prayers intentionally missed are lost forever and, therefore, cannot be offered after their prescribed previous times. a person has no other option, except to repent to Allah and ask for His forgiveness and mercifulness for all the prayers that he has intentionally missed in the past be forgivnen by the All-Merciful.
I would be more inclined to lean toward suggesting a combination of point number 2 and 3. My suggestion would be that you pray your regular obligatory prayers, offer supererogatory (nafil) rakahs regularly and seek Allahs forgiveness for your past. It may be hoped that your supererogatory prayers and you or anyone for that matter who consistently seek Allahs forgiveness for your past negligence toward prayers, shall insha'Allaah, be a source of complete forgiveness and infinite blessings for you and all of us in the hereafter from Allah,ameen.May Allah help all of us with this,ameen.Insha'Allaah brother,keep myself and my family in your duas as you and yours are in mine

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Allah knows the best in all regards of aspects.