To the OP you may be interested in this as it is similar to your set up.
I am pleased to report that my current set up for venting as mentioned in a previous post has worked out very well. The chooks are currently housed in my main building. Area for chooks is 8x16 but vented closed in area is 16x16. This has been a really great past week to test the venting of a coop for my area. Outdoor Humidity levels have ranged from 80% - 16% all within approximately 48 hours. The method I am currently venting this building with is using a 1/2" gap in the soffits along the perimeter of the building.
The only high exhaust is a cut out for a power roof vent. Cut out is approximately 14"x14"
I do not have any other real intake or exhaust areas beside my pop door which for the winter I reduced it's size down to 12"x12". I currently have 10 hens and 2 rabbits housed within that area.
With this setup I have been able to keep the inside of the building the same if not better than the exterior of the building. Here is a snapshot of my monitor to show you the extremes over the past few days. I believe it monitors and shows the range over a 24 hour period. Humidity high was 75% inside and low of 16%. Actual humidity was well above the 75% but building stayed below.
With this method of venting which is very similar to the OP has worked really well. Normally I would have done a ridge vent and called it a day but I think in the summer the power fan is a much better option. OP keep an eye in the summer. I do not have any noticable air movement at "occupied level". If your coop is big or small only way to really tell is by being able to monitor the actual levels.
Here are some other pictures for reference.
You will need to keep your roof vents clear in the winter.
I am pleased to report that my current set up for venting as mentioned in a previous post has worked out very well. The chooks are currently housed in my main building. Area for chooks is 8x16 but vented closed in area is 16x16. This has been a really great past week to test the venting of a coop for my area. Outdoor Humidity levels have ranged from 80% - 16% all within approximately 48 hours. The method I am currently venting this building with is using a 1/2" gap in the soffits along the perimeter of the building.

The only high exhaust is a cut out for a power roof vent. Cut out is approximately 14"x14"


I do not have any other real intake or exhaust areas beside my pop door which for the winter I reduced it's size down to 12"x12". I currently have 10 hens and 2 rabbits housed within that area.
With this setup I have been able to keep the inside of the building the same if not better than the exterior of the building. Here is a snapshot of my monitor to show you the extremes over the past few days. I believe it monitors and shows the range over a 24 hour period. Humidity high was 75% inside and low of 16%. Actual humidity was well above the 75% but building stayed below.

With this method of venting which is very similar to the OP has worked really well. Normally I would have done a ridge vent and called it a day but I think in the summer the power fan is a much better option. OP keep an eye in the summer. I do not have any noticable air movement at "occupied level". If your coop is big or small only way to really tell is by being able to monitor the actual levels.
Here are some other pictures for reference.


You will need to keep your roof vents clear in the winter.