What evidence have you seen that suggests they could get a premium for your place whilst still selling in your timelines? I would be looking at the land registry and their comparable sales closely.
It might be that I've mixed your place up with somebody elses on here so if that's the case ignore the next bit.
I'm going to play devils advocate here - I would imagine TMH and whatnot could get a premium for properties that are not easily, or cannot be, replicated or equivalenced. True one-offs. Because their market really is niche and because their value is market + nebulous but large cachet from owning a concrete masterpiece or living in the Barbican.
For flats, and this is what we are talking about right, in nice but ultimately 'common' buildings, I'm not convinced they could command a significant premium compared to figures the high end EAs or indies could get. Because what you have , which IIRC is a flat in a victorian house - can be recreated or equivalenced*. I think their fee - which is expensive but not an unusual starting gambit from even the hightstreets - is probably an admission of that.
So I would be inspecting their patter and comparable sales closely.
But I could be completely wrong.
Related, Nested looked at my place the other day and totally ballsed up the valuation. Then pestered me.
* The award can't, and that is interesting.