Those joists are blowing my mind! Not only the span and the spacing, but the nailing plate joining two pieces of joist together (you left that little detail out, before
)!!! So you are storing a lot of balloons and bubble rap up there?
I'm looking at the position of the door and the partition wall...you can't flex a 2x6 (shorter than writing 165 x 45) to get it in? Take the door off if it is in the way. Personally I would scab a full length 2 x 6 onto the existing 2 x 6, or even a 2 x 4 to beef up the existing joist (2x4 would clear the blocking and DW)...while it is open. This would be glued on with construction adhesive and screwed with #10 x 3" screws (on a bit of an angle so the point doesn't come through) in a "W" pattern with a 12" OC. Pull them together with a threaded bar clamp before screwing...and move the one or two clamps along. If you really can't get a full length in, use the longest you can and scab it to cross the nailing plate. Usually I try to get the length between the walls, plus the depth of one pocket. Get one end up and in and the other end up and slide it back half the pocket depth. In a floor application, I would use 3/8" carriage bolts in W pattern 12" OC with glue. For your needs the screws are enough (you are adding to something that is already staying up!)...and cheaper...and faster.
For the new ceiling joists. A double 2x6 is more or less equivalent to a single 2x8 for loading. I had a ceiling on my upper floor that the previous idiot had decided to use as floor in an attic conversion. These joists were actually the collar ties for the roof rafters. This space was used as a bedroom for tenants renting the floor. These collar ties were only 2x4!!! Yes it was shaped like a saucer. But it did not come down. Did I mention the span was 16'?
If you could get a full length 2x6 in, long enough to sit at least 1 1/2" on each new wall, you would probably be OK holding OSB or MDF and two layers of DW if you could use a 12" or 16" OC. Double 2x6 if you are stuck on 24" OC. If you can't get the full length in... Use the longest length plus filler and laminate a second layer, reversing the joint. Glued and screwed. Build these on the floor and raise them up into the joist space on their sides and store them there (with sky hooks
) while you build the walls. This way you don't have as much fighting to get them into position with the "smaller" room.
What was that about the white smoke from the first BBQ of the season? Seriously, you don't BBQ year 'round? I have heavier cotton T-shirts for winter. I thought Swedes were tougher than that!