To come at it from someone who does work in a supposedly fulfilling sector- the pay is a lot less, there is a lot of stress, but you get satisfaction. Make of that what you will.
Does more money make up for low satisfaction? I'd say yes it probably can - but you need to consider - are you going to spend more money outside of work getting satisfaction? No right or wrong, but say you need to spend 12k on an exotic holiday to prove this is all worth it - if you want the holiday, fine - but if it's something to show for it, I don't know. You need to address the question of what gives you meaning.
Does more money make up for high stress - I don't think so. I've had slightly higher paid more stressful jobs, and they weren't worth it. But, how much less money is doable? I've found a 5% drop made no difference, I've just got better at budgeting and I'm happier.
But if I went even lower in salary...not sure I would want to choose that. But sometimes life decides for you - ill health etc.
There's some good advice here about making it work for you - I would add things like buy more annual leave schemes, any opportunities to work while abroad, any opportunity to take a sabbatical, working hours that suit you, dropping down a day if you can afford it, are sorts of things to look at too.
Completely switching - I did that in my early 30s and it was a lot harder than I thought! If I'd known maybe I would have done things differently. The challenge is that it gets harder to learn in your 40s - not impossible to do something new, but mental energy at weekends to process.
Other things to think about - prospects in your industry. Are you going to face redundancies later on, and if so what might you choose to do and can prepare for? I work in an area that is likely going to change and I'm not sure what it means yet, but am thinking that I need to build my network.
And lastly (been looking at this in early 40s) is FIRE - Finanical Independence Retire Early. Its things like getting finances in order, budgeting, investing in what I value, sorting debts and savings, working out what my pension is invested in and how to maximise it, working out when I can retire. You could go full pelt at FIRE'ing, or slower and enjoy fruits of life along the way.
For me I spent a lot of time early on in my career working out what I like doing, never focused on money, so probably going to work longer. At the same time I was very driven and a workaholic. In some ways - and still for me - its a lot harder to switch off when you are passionate about your work, but if I'm gonna work longer then work life balance is key!
I'm considering moving to cheaper property so I can have less mortgage debt and put more into my pension pot, as any money invested in my 40s also has more time to grow.
Edited to add think there are a growing number of career switchers in their 50s - those who've either faced redundancy, or are looking for something more meaningful, or realising they may need to work for longer to retire.