Yeah i been in your situation ...
You got two goals
1.) To delute the bad history with Good
2.) To get rid of as much bad info that you can via PFD and/or GW
If you are really not wanting to go with a cosigner which may or may not be an option for you at the moment. Your main focus in the months or year(s) to come would to show some positive payment history... meaning on time payments consistently but unfortunately if you are trying to secure an apartment very soon this takes time. You should know atleast you should PIF monthly and stay on top of your balance for the secured car regardless of whether you chose to get a cosigner so you can become more financially independent in the future.
Your other task would be to clean up as much of your report that you possibly can. Meaning that if your other derogs you mentioned are co/ca's unpaid you can try to pfd them or if they are paid you can try to GW them.
With the car loan you kinda waited a little long becuase you only have another month of it being active. You would very much like this TL to keep reporting but you want it to report in good standing. It can help towards securing the next auto loan if is reported positively. You became a month behind and then paid timely however you never caught up that month that you missed is what i understand. Just explain how you got behind and did your best within your budget to keep the payment from getting any further delinquent but you may have lacked the resources to get the loan current. This may or may not fly because you could have paid a little more than the monthly payment due to gradually make the difference over the course of say four months or so ( just an example). If it is a single isolated 30 month derog than you may have a much easier task of getting them to forgive it. Keep in mind you want this one to work for you because it can become crucial for any consideration given it's recency. However you may not want to wait 7 years from now for this one to report in good standing.
The student loan however you can request a GW to delete this account. Erase the TL entirely. Explain the circumstances that got you delinquent on the account and that you since made good. Keep in mind this tradeline will be permanently deleted if they agree to and will not count towards your aaoa after this happens but you will have the advantage of not having a default loan on your records and when it all said in done you may end up looking like your history was great in the past few years without even ever getting any of the older five year old blemishes off. (keep in mind you would like to get rid of these too ... however by focusing on the car loan and the SL you can show a postive portraiyal of recent history 
)
I've been in your situation before and what you're doing right now is journeying toward financial indepence so you do not have to rely on others to make moves such as this and gain a peace of mind... Good luck.
Great Info thanx!
Starting Score: 470