You sure do have plenty of space up there.
The joists you have there now are engineered I joists. Not really made for what they are being used for. They have a tendancy to roll, and the connection in my opinion is not as good as a solid 6x6 you could get in there.
The upper collar ties need to be 1/3 the way down for the ceiling to do any good structurally. This is just a basic start, it really depends on your snow loads. Where I am this is minimum, as we get heavy wet snow..and sometimes lots of it.
this is just a start, to get what you really need and to stop the cracks in the ceiling which will occur from getting larger over time. You need an engineers advice. This will most likely be a couple hundred dollars, well worth the price for heading off any issues later, and a good piece of paper for when you ever sell the house.
This is absolutley a diy job, just get a good start...and you will sleep at night.
The engineer will give you lumber size,distance from the floor to ceiling, fastener size and how many beams to put in where they count.
Good luck, hope this helps.