It's your car so you can hold out for whatever price you like, that's your prerogative.
You do need to watch out for your justifications though as they don't stack up against the way cars are valued. The condition, servicing, tyre condition... that doesn't increase it's value in the market, it simply increases the dealers margin if it does got through the trade. Also, 15 miles is pretty restrictive when considering your local market conditions. You need to double that and some to be confident it is good value to others in the vicinity. (Just saw your note about the 50 mile range. The 1.5 is definitely favourable over the 1.0 but I'd take the 1.4 over both any day of the week!)
TBH I'm surprised we are even talking in the realms of 18 to 20k for a standard crossover hatch that doesn't even have climate control but that probably just shows how out of touch I am with car pricing. Anyone who bought cash circa 2018/19 must have had some pretty depreciation free motoring. Problem is it's like houses, you never really see that gain (or in the case of cars, reduced loss) unless you sell and move into a cardboard box.
I say all this as someone who massively prefers to buy private so I really do want you to do well with the sale but expectations may mean that the potential BMW purchase simply isn't possible right now.