Sorry, OP. I am a teacher and couldn't agree more that it is a lot. It won't get worse though, in my estimation, as the school is trying to maximise their pass rate for the phonics screening check at the end of year one. You might find the urgency drops away a bit after that.
There isn't much evidence that spelling tests work in the long run unless it is a word that the child will write regularly after the test, so try not to worry.
My daughter didn't have spellings in Year 1 as it was pre phonics check but what I would do is make it quick and fun. Get some post its or blank bits of card, write the spellings on and get DC to sort them by sounds. Which ones have got ir? Make it visual/colourful and move things around. If you have any magnetic letters, use them to make the words and pull out the target sound like 'ir'. Practice just those one day.
Get some different coloured felt tips, write the bits he is getting wrong in different colours. Write them in chalk on a wall or patio in the garden, on a mini white board etc. 5 minutes a few times a week is better than a long slog before the test. Also, use time in the car. Ask him what ir sound is in bird. How do you spell 'come'? Say the letters in a silly voice or whisper the letters in 'quiet' when you get that far. He'll have ideas about making it memorable.
It might still take a bit of time but it might not feel like it and he'll be keener to crack on. Stick the post it notes in random places-get him to do it. Send him to collect them the night before the test and ask him which he thinks he knows. Which ones are still tricky? Practice those. Stand up and say the sounds while stamping a foot for each.
Whilst the ideal way to read with your child is sitting at a table next to them so they can use their hands and the book is still to aid tracking, I read with DD in all sorts of places, her sat on my knee with the book on the steering wheel when trapped in the school car park at the end of the day was a favourite. I know lots of parents who drive to school and do this waiting for the door to open. Kids are often fresher in the morning. I am not, so we didn't do this, but might that suit you guys? She also read her book while I cooked/emptied the dishwasher.
Tell him he is doing brilliantly at every opportunity. I don't get very involved in homework now she is older but maths has suddenly got a bit tricky in year 10 and it is nice to sit next to her and do it together at a time when she doesn't really need me very much any more. Reading with and to your child is the best possible thing you can do to ensure they do well at school so that would definitely be my priority.
You are completely right though: we are asking a lot of Year 1 parents. Tell yourself you are doing brilliantly too.