If you're not tied in, I think I'd move agent.
The fact they don't seem to do floor plans as standard (trying to save money?) is such a bad idea in this day and age, plus the fact they've tried to justify it and persuade you it's not needed, just means I'd have lost all confidence in their professionalism.
I'd be going elsewhere and telling them exactly why.
At the same time, I'd be considering the price.
You mig have had 3 valuations or whatever, but you can see that similar houses are cheaper and bigger ones available for your price. Therefore you can see that yours is very much at the upper price end/over priced. This will be a key factor in why you aren't getting more viewings.
Yes, it is very nicely presented. But there is still a ceiling price for everything and it is still a 3 bed where it is and is unlikely to beat the prices of 4 beds.
You can hang on at the price you're asking if you want to. There's nothing to stop you doing that if you're determined to squeeze the last penny out of it....but it may well slow down getting a buyer.
Moving agent and the price are 2 separate issues here. You can do 1 without the other.
How much below was the offer? If you do t want to say exactly, can you say if it was extremely close to the asking price? You clearly accepted it so will go below the asking price, so how about considering marketing it at that price? If you do drop the price, be prepared to go for a credible drop (ie not just £3k) ....it's always disappointing when you realise your property is over-priced and you need to lower price, as then you might not even achieve that fully....but this is the way of property markets. Ultimately depends how urgently you need a buyer, but if you hang on at the current price (regardless of agent) and find in 3 weeks that viewings are slow and/or no decent offers, you really will need to lower price. Be realistic about what 3 beds in your areas (even very nicely presented ones) are getting and don't be too ambitious. You can check Rightmove like we can and see yours is at top of price/over-priced....and all the prospective buyers can see the same.