Agreed value insurance questions

[Streets]

I have searched here for recommended insurance companies and from the sounds of it, Lumleys or Ryno is the way to go. However I have never insured a vehicle full comp before so I am unsure of what to ask for (ie, little things that I might overlook). Basically all the special features I'm after is choice of repairer and retention of wreck.

The car is a 1979 XD, 351 with ported heads, Edelbrock manifold, Holley 650, custom exhaust, lowered suspension, shaker, multiple killswitches. I am 24, turning 25 in March. I've spent about 10,000 on this car over the years (not including purchase price), but of course I realise that it's not realistic to get all that money back if something happens.

I don't really know what is a realistic agreed value for the car. I would like between 10-15k, but in the online quotes I've done, it has said "value is too high". In the topic I searched for, people were insuring their cars for 20+k. Is 10-15k too unrealistic for this car? I thought the idea was you gave them the sum you want it insured for and they tell you how much it's going to cost.