The house could have gone up in value to 450k during that time.
I used this:
https://www.nationwide.co.uk/house-price-index/
I put in valued at 345k Jan/Feb/March 2019, asked for its value in Oct/Nov/Dec 23:
I put in specific postcodes of areas I know.
Where I live, NW: 441k
Used to live, Midlands: 427k
Used to live, SE (ropey): 399k
The asking price might not be as unreasonable as you think.
Of course, you're perfectly entitled to offer whatever you want, especially as it's been sat on the market for so long.
As to alienating EAs... that's a toughie, they can be 'special.' Put it in writing on an email, don't haggle on the phone, don't explain your decision/offer. Don't say 'we only think it's worth' or 'they haven't done anything to it' or similar, just state your offer, because EAs are trained to box you into a corner for ANY explanation you give in response to a lower than asking price offer, it's literally their job. So. Don't phone.
but I’m cautious as the last time we offered 15% below on a house we liked the EA basically cut us off.
Don't let it get to you, is my advice. The other EA may well have 'cut you off' but I promise they'll be back in your life as soon as you look procedable on another property of theirs. You have to seriously piss an EA around to be 'blacklisted' and I'm sure that sort of thing only really happens in a frantic market when they can pick which buyer to recommend.
It could be that regarding that particular house, they'd overpriced it, and were getting fed up with people lowballing, because it makes them look incompetent.
Either way, don't let it be your problem.