So you have 5 only 30 day lates is what you are trying to say because if you are under the 30 day late like you just paid a small late fee but you never went into the next month that won't show as a Late on your CR.....If you are hoping for a Home Mortgage you are not trying to buy in February are you?! The main things you will need to rid yourself of is the collections and the accounts you do have in good standing is good you just need to make sure you do like you plan and get them both under that 30% utilization under 15% would be better but removing those collections would give you a good boost and whatever you do do NOT apply for new credit/accounts 6 months before applying for your mortgage unless you applied for your current cards recently that can't be helped but be sure to include that in the 6 months so if you got those this month?! Then I would apply in June after removing Collections but I do need to know what you mean by the 30 day late part 
The charge offs will report monthly until paid or settled. They will fall off in 7.5 yrs. So you close to seeing them gone. Some cases as a last ditch effort. They may persue legal avenues to collect before they are gone. When you payoff the last account for NFCU. They will give you a second chance maybe with a secured card. Least you wont be blacklisted. Thats a good thing. Lastly since you have 2 cards. Always have 1 report a small $10 balamce and the other one 0 balance. In FICO's eyes all your revolvers are reporting a balance. They like less than 50%.
You could try without knowing your scores for the Disco secured that will graduate in time. Then you'll have the 3 cards that helps rebuilders scores. But the CO's will still hamper you until they're gone. You have the car loan so no installment loans are needed. Thats about it. Good Luck!
