The recency as well as the severity of your delinquencies are impacting your score.
If you have major delinquency 90,120, etc. day lates, they will keep your scores supressed for entire time they are on your report. You might see some relief once it ages to 2 years.
As you've experienced, the monthly updated collection has kept your score suppressed. You won't see score improvement until the last collection has been paid.
If you can do PFD Pay For Delete, that would be great.
It's recommended to have 3 open revolving credit cards and 1 open installment (mortgage, student) loan for score improvement. Based on your scores, you'll probably need a secured card.
It's also recommended not to apply or obtain any new accounts 12 months leading up to a mortgage. So you'll have to time your application. You'll see a 10-15 point increase when AoYA Age of Youngest Account >12 months.