Florida13:
I pretty much agree with all the advice you've suggest been given.
The effect of 60 day lates will decrease over time; the 90 day lates will carry the full impact until they come off. Additionally if these are federal student loans, that could be as long as 10 years or the life of the loan. These same special regulations for these federal student loans require that they be reported accurately. Unlike a credit card or an auto loan, you will likely get nowhere asking for a goodwill adjustment because they aren't supposed to give it to you. You could try, and I think the saturation technique would give you the best chance, but I don't think it's the stress to focus on. You can still obtain a 750 with a 90 lates if everything else is ideal.
I would focus on the collections. PFD is obviously ideal, but getting them paid is still great. I was helping someone with a thin file try to raise their score. Adding them as an authorized user on a card with >5% until, 3 years old, 0 lastes was helpful (I kept their card). You might think about this if you know someone that will add you, btw. It was the removal of two small collections that raised his score more than 100 points.
Another thing to note is that if you're going for a FHA loan and you have federal student loans, switching to an IDR plan has additional benefits in how they calculate your financial obligations. You can search on the mortgage threads for further information.
One last suggestion, as you're getting closer to the date make sure to get an ok before you try to make changes on your credit report. For example, I've heard that disputes can be a bad idea because of how they temporarily remove certain parts of the tradeline from calculation of your score.
Good luck and feel free to ask further questions.