2x6 Cathedral ceiling options

[Juststarted]

So I have done plenty of research on this topic and haven't found all the answers I need. The usual disclaimer: I am not a builder by trade and do not know all the correct terms. I bought a single story ranch last year. There is a bonus room that is built on a slab. This room had a half cathedral ceiling with very strong mold smells. Tore the room down to studs to find foam board insulation just pressed against the underside of the roof with mold from lack of air flow. I would like to put this room back together with a full cathedral ceiling. The rafters are 2x6 and there are no collar ties and just a few 2x4's as joists in the area that wasn't cathedral. It is a smaller room (15x11 ish). The peak runs in the long direction of the room, and the rafters are angle cut and set on top of the walls (common rafter construction).

I am on a very tight budget here and this home is not a forever home so it doesn't have to be the best insulation job with an R5000 value like I see some people trying to achieve.

Foam insulation, I am guessing, is out of the question due to cost.

I can either furr out the 2x6's or sister them. What I am unsure of is where the wall line meets the ceiling line. The only options I see is to either shorten the wall by carrying the new ceiling line down at the same angle as original, or taper the new rafters in at the bottom creating 2 different angles as you go up the ceiling line.

I am not trying to meet a specific code R-value, just trying to make the room comfortable to live in and as an added bonus.. mold free.

I have also read some comments of doing a partial cathedral ceiling, where you leave the 2x6's and insulate accordingly. Then in the flat area of the ceiling, insulate more. This method assuming the angled portion of the ceiling acts more like the walls in heat loss and the flat portion the true ceiling area. Not sure how much I buy this.

Thoughts? Opinions?

I know it would be best to bring in an engineer ect ect but that is not an option here. I already plan on making the room stronger by adding collar ties that aren’t there. The room has been standing many years without sagging so I am not too worried about any issues with that.

[Don_P]

You could install soffit and ridge vent, air chutes in each bay all the way and R15 batts. Underneath the rafters install foam boards, offset seams between layers and tape all seams, then 1x strapping screwed thru the foam to the rafters to support the finish ceiling.

The ridge should incorporate a beam capable of supporting half the roof load with the walls taking 1/4 of the load each. The beam would then need to be supported down to adequate footings.

What is the relative humidity in the room?

[Juststarted]

After some other posts and thinking and measuring that is the way I am leaning. I am unsure of the humitdity in the room and don't have any way to measure it. I am in the Boston Ma area if that helps.

As for the ridge beam, it is just a 2x6 as well. One side is supported by the original roof and the other is not supported all that well. I have added some pictures.

I plan on putting collar ties/ceiling joists in. It won't be a full cathedral ceiling and will be much stronger than the current design.

[Don_P]

It looks to be isolated from the house... I'd be looking for the source of the moisture that caused the mold. You can pick up a thermometer/hygrometer at a big box store for ~$20 and get an idea of whether there is an elevated humidity level in there. Is the slab sealed?

The penetrations of the ceiling joists/rafter ties are tough to seal well and a common source of infiltration.