Rockybalboa:
Several things.
Do you bath your DC nightly? If so, would reading school book/ books from library or home be a nice thing to do just before bedtime - say for 15 minutes or so?
I note that you say: he tends to just want to play or veg out in front of Netflix for a bit as soon as he gets in
I get that kids like to watch cartoons and relax - what kid doesn't - but perhaps the solution is to offer this as a reward. Read with me for 10 minutes while I wait for the pan to boil, DH to get home, etc... and then you can watch tv/ play video game/ etc....
I get that your DC is tired at the end of the day - my DDs were as well in Y4 - but gradually - especially as evenings grow longer this Spring - you'll probably find your DC has more energy.
With reading at night - are you having him do all the reading?
Have you considered sharing the reading. To encourage DD1 (who really struggled to pick up reading skills) - I started with her picking out 'key words' - The, and, but, this, that, or, may, saw, said, etc.... So I would point to a particular word we were working on - say 'The' - and have her say it each time I saw it. She felt she was reading - and we just kept adding more words until gradually we worked up to her reading a whole sentence. Once she could read sentences, I'd agree that I would do the rest of the paragraph if she read a whole sentence correctly.
Once she was good with sentences - I had her read a paragraph and I read the rest of the page, if she had read it well (maybe 5% or less words slightly wrong or skipped - she has a real thing about skipping words).
On nights she was just plain worn out - I did the reading. Listening to the spoken word is also important. If you're reading try and use your finger on the page so they can follow the words you are saying.
Eventually, to encourage DD1 (who often got things wrong) I played a game where I'd say the wrong word and she could correct me. She really enjoyed that. So instead of 'said' - I might say 'stated' or 'announced' - and she'd get all excited and explain what the word actually was.
As your children get older and start reading themselves - you may find that reading to one whilst the other is having their bath is a nice way of dividing and conquering.
HTH