Rafters with no ridge beam

[Kelly S]

Bought an old farmhouse. Am a "do-it-yourselfer." Would like to insulate the roofline with Icynene, but need to make sure the roof can handle a snow load once insulated. (No insulation now, so no snow stays for more than a day.) Live in Kansas. Have been reading this forum, and have great fears.
Here's what I have:
One section of the gabled roof is 34' from gable to gable, 24' span across, with knee walls at 6.5' from both outer edges. Knee walls are constructed of old, true 2x4's but the uprights are spaced every 4 '. Here's the real kicker. The rafters are 2x4's (newer ones 1.5 x3.5) on 24" centers, notched (think you call it bird beak) at top of walls, but NO ridge beam or board. The rafters are simply toe-nailed together at the peak.
I believe the pitch is roughly 8.5/12 (Peak is 8'5" above floor and 12'/2" from outside wall across floor).

I was hoping to finish this room, using the knee walls and gable ends as the room walls, and attaching drywall to rafters. Can drop the ceiling a bit down the ridge to allow for collar ties if that would help.

What do you think? (she asks with a clinched teeth grimace)

[Cole]

Welcome to the forum.

How far can you come down with the collar ties?

[Kelly S]

Well, if I dropped the peak from 8'5" down to a ceiling height of 7", that would allow the collar tie to be about 18" long (if I'm figuring that right).

[Cole]

In your case, that is all you are going to be able to do.

Unless you want to tear the roof down and start over.

lol

[Kelly S]

Really didn't want to start over, lol. What about adding extra 2x4 rafters from the peak down to the knee walls. Can that be done and would that add to the structural soundness of the roof at all?

Oh, and thank you for the welcome.

[Cole]

That would probably just make it heavier.

The collar ties will be fine.

[Kelly S]

To make matters worse, just realized that the knee walls are not situated on walls underneath. They are simply laid across the floor joists (perpendicular to floor joists). The good news there is the floor joists are 2x8's on 16" centers.

There is however a supporting wall that runs the 34' length 4' in from one of those knee walls. That's puts it 10.5' from exterior wall (roughly 2' off center). What about some kind of beam running across the bottom edge of rafters supported by columns positioned on top of this supporting wall?