I would consider dumping the methadone or take them first. The reason I suggest this is methadone has the highest half life. Opioid acute withdrawal comes down to a pretty standard equation. 5X the half life of the last opiate taken plus around 3.5 days before you will start to feel noticeably better moving forward. Methadone is commonly misconceived as preventing other opiates from working. This is not the case.. it's just a very powerful agonist. Other agonists can an will work especially given an average of over 8 hours.
Unfortunately everyone who travels our path pays the piper. The path out is the acute withdrawals which are close to 5X the half life of the last opiate ingested plus about three days. Unfortunately we can't use opiates to detox opiates, because every time we reintroduce an opiate the detox clock starts over.
The equation is this... Acute withdrawal, post acute withdrawal and psychological addiction. Imho to successfully "sneak" outa hell we need to successfully address all three. Break all three down into easily addressed micro topics. PLEASE PLEASE remember if you relapse after any amount time your tolerance to such powerful substances will be so severely reduced that you will be very vulnerable to overdoses death.
You can do this!! If I can do it anyone can.. over a decade at this point and I don't even think about it.
Please make sure you and your people have narcan while you navigate your way out