Two schools of thought on the butter for the Brioche. Many formulas call for retarding the dough a long time or overnight. For these formulas you use room temp or soften butter.
If your not going to retard a long time, the butter should be cut into small chunks and as cold as you can get. This way the friction of the mixer or your hands does not melt the butter.
Honestly, no oil in traditional Brioche.
A little milk is also very acceptable.
If you use the softened butter and mix to long you end up with a slack dough, making it dense.
Always do a windowpane test with Brioche, especially when the percentage of butter is increased.
I think traditional Brioche is one of the best finished products. It might take a couple of times to get what you like. It can be very
versatile, hamburger rolls, chicken salad, bread service with a gamy protein, etc. and like rpooley mentioned, the best French toast ever!etc.
Don't give up on it, it's a great formula to have and pass along. I wish I had a scaled down version to give you but mine are for a minimum
BTW, your braid looks really nice and it good to hear you had the courage to try an old standard.