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You have some secured cards, which is good.
All I can say now is that since everything is current, start a GW campaign to have the lates removed.
Here are some posts about good willing (GW):
If these are private student loans then trying to get them removed via goodwill letters is a good plan. If they are federal student loans, trying to get lates removed via goodwill letters will be futile as the reporting of lates is required as a matter of law (Higher Education Act).
On the bright side, the collection accounts are probably having the biggest impact on your score. Hopefully you're able to get PFDs on them. If not, paying them will stop them from updating every month which will allow your score to recover over time.
Here's a graph that another member created showing the effect of lates as they age. It looks like your scores will recover ~20 points about six months after the lates. According to the graph though the presence of any 90-day lates has a big impact on your score for the entire duration of their time on your report.
I would encourage you in the future, if you run into any financial hardships to contact your servicer ASAP to see if they can help you (by getting you into forbearance or changing to you to an IDR payment plan with a low payment, etc). I made the same stupid mistakes and now I'm paying for it with multiple 90-day lates (and some 120-day lates on my Perkins loan ). My loans are currently on a $0/month "payment" plan and the process to get it was not too onerous.