You could try the cold turkey and see how it goes?
Or you could try adjusting a bit slower. I have a similarly screen-attached DH, and if I'm totally honest I am internet addicted too, I have to really resist it almost all of the time.
With DS1 (now a teenager) it was unlimited partially because I had vague notions that it was cool to let kids self-regulate (lol - that never happened) but probably also because I was a bit overwhelmed when he was younger. When he was about 10 and we were getting him assessed for ADHD and they queried the screen time, it was like a massive lightbulb moment and said OK this has to stop - cut it down to 3 hours max per day and this did improve things hugely. I think because previously, I'd been too wimpy to cut it down properly because any time he was off the screen he would be absolutely impossible, flopping and moaning and complaining about being bored, asking if it was screen time yet or what jobs he could do to earn screen time - he was obsessed and it drove me absolutely mad.
Once it was down to less than 1/4 of the time he was awake, it seemed to flip things the other way around, where rather than spending every non-screen minute obsessing over the screen, he stopped doing that and actually engaged with other things, which was a huge relief.
Once he got to age 16 he asked us very nicely if we could take the limits off, since none of his friends had limits and he believed he was more responsible then. He was out a fair bit at the gym/with friends/at school so we said OK but kept a bedtime limit on, since he's prone to staying up late and it affecting school otherwise. (BTW - he did end up getting the ADHD diagnosis anyway at age 13. They do not think it's screen related - the doctor said it's probably the opposite way around, that the ADHD makes him more likely to be drawn to screens.)
DS2 & 3 (7 & 4) came along and then of course there was the pandemic. When they were really tiny the TV was on so much of the time. DH insisted this was fine because they would just play around it and ignore it - OK. But then they started getting older and I really didn't want to fall into the same patterns so we got into this dance where I would constantly be trying to turn the TV off and DH would constantly be putting it on - it's like he's afraid that if he is not entertaining them directly and the TV is not on, it's terribly unfair and cruel to them, which I don't agree with.
It really sorted itself out more when we moved and I was home 24/7 with the DC before we got them into new schools and I just had a rule of no screens within certain hours and a max amount of time per day on the console which was a much lower limit than DS1 ever had. We also have an old phone with games on but I keep this and they get access to it occasionally using a timer, but not every day.
Then I instigated a rule that we do NOT do screens as the first thing the minute we get home. We have to do at least 1 other thing first. At first this was just a quick game of Uno or something but as they got used to this, it branched out to be more involved playing and some days they didn't even want/ask to go on screens until dinner, where unfortunately they are still used to watching TV. But it's much better and weekends aren't just a constant screen fest. There is still a lot more screen time than I'd like at weekends, but since we've come to a norm of majorly reduced screen time during the week, DH is starting to see this as more the norm as well - it also helps that since I've instigated this, you can absolutely see a difference in their behaviour on the too-much-screen days - DS2 gets really hyper and silly, whereas DS3 won't go to sleep at bedtime unless he's had a bit of a run during the day.
DS1 is fine - aside from the ADHD (which is probably genetic anyway as I also have it and so does DS2) which is fairly mild for him, he does well at school, he is social and has IRL friends, a girlfriend, a job, he goes travelling, he has hobbies, he is generally doing fine and actually makes me laugh with how sceptical he is about AI and social media/microcontent. So I am not especially worried about any long term harms of screen time. My major focus is how unpleasant it is when they are basically so used to the screen that they can't cope without it or can't seem to entertain themselves without it. That, I really don't like and find incredibly draining to manage, as well as it being too easy for me to slip into bad habits of too much computer time, so I prefer to limit the screen time to a level where we avoid all of this.