While healthy, the diet may be a little drastic to start with.
What I mean is, if you are used to 350g carbs per day as an example when you were overeating, than you can probably lose weight on 250g carbs per day. But it would seem that your carbs are already very low.
Your diet is obviously healthy in terms of food selection; good sources of protein and healthy fats, no processed foods, includes fresh fruit/vegetables, etc. Therefore, the issues at the end of the day will be 1) total calories consumed vs. total calories burned and 2) what your exercise regime is like.
Regarding #1, I woud make your caloric deficit 500 to 750 calories to start based on your current diet. That should give you room to bump down calories several times when you get stuck.
How long have you been doing the current diet? My concern is that it is too low in carbs/calories and that when your weight loss stalls (which it will), you will have no options.
I would add the oats in as you asked about.
Regarding #2, make sure you are doing some type of weight training to tell your body to maintain muscle while in a caloric deficit.
James 1:16-17 ESV
Do not be deceived, my beloved brothers. Every good gift and every perfect gift is from above, coming down from the Father of lights
With God's help...Mens sana in corpore sano