If you want a true blackout option, blinds are not going to work very well. I'd go with either a blackout roller shade, or a roman shade with a blackout lining. You'll still get some light seepage on the edges, so you could add drapery panels on either side of the window to mitigate that.

I have those exact blinds in a get-away little place and you're right, they don't block out enough light, especially when you want to sleep in for once and your windows face the sun rise. Sigh...

I have the wood ones at my home and they do a decent job - my windows are angled on the corners of the room and face roughly 280 degrees west and 20 degrees north - I literally just used the compass on my phone and I would have said my windows were NE and NW. But I digress....

Something you might like is something we did for my mother-in-law some years ago in her piano room (the 1969 era living/dining room) that faces westerly. We bought her a cellular shade that blocked the sun and the top could be let down and/or the bottom drawn up. She could adjust it to however, to maximize the light and keep the sun rays/heat off that can discolor the black lacquer piano. She's a music teacher and it afforded privacy as well from the street.

She loved the top down/bottom up feature so much, we got her black out ones for her bedroom.

Get rid of them. First, look at the stack that blocks any light coming in during the day. The blinds are super heavy and each time you operate them you worry not to rip them off the window. Unfortunately you cannot get them light sealed.

You need minimal bottom-up top-down black out honeycomb shades. The fabric is black out and form follows function. You can move the shade to any position of the window and the stack can be on the bottom or the top but will be much less than you have right now.

The light gap between the window jamb and the shade is approx. 1/16 inch on each side...very little light can come through.