Tosh
I always quote what I see (as mentioned), any work you get as an addition, in the future, will be a bonus.
Again you have enough experience of what you expect to achieve as far as a day rate. Do you need to compromise on the price just because you might get more work in the future.
I think that if you have a sign written van, that is clean, turn up in a clean uniform, are pleasant and professional, can hold your own in a conversation ( with your background there shouldn't be any problem there) and offer a flexible quote, then there is no reason why you shouldn't walk away with the work.
Flexible quotes are tiered and I like to use them because if the full price is too much you haven't closed the door by only putting in one, non flexible, price.
Give them multiple quotes in one, break it down so they have somewhere to go with it.
If you want to give me a call and have a chat I will be happy to run you through how we operate. 07919 425664
I have multiple price structures in place, for all the different services on offer and they are all at the level you are looking at.
Don't drop your standards and never offer a half clean or sooner or later you will get the big one but someone like me will come along and have reason to edge you out of the works.
Give the client no reason to fault your end product, give them the best service they have ever had, for their money.
Good luck
Rob