Finaly getting my crap installed.

So i finally got my car into the shop to install the following:

GT2871R Turbo
Injectors
42draft 3" downpipe
3" APR Car-back Exhaust
Full Samco Turbo Hose replacement Kit

well i took my car in on monday morning and my shop quoted me $438 to install everything except the Samco Hoses...
and maybe $75-$100 for the Hoses...

Today i went in to the shop to check up on the progress and i was stunned because they were having a very hard time getting the turbo and manifold off. They said they spent all day trying to remove it and even went to a audi dealership near by to price a quote on the removal if they weren't able to do it. Audi said $2200 for the removal and replacement of my parts, so the guys told them hell no and kept working on it themselves. When i was there they had finaly removed the bolts and everything was finaly out. I over heard some of the guys saying that the job has costed them more time then they had expected obviously hinting at charging me more money for the extra work they have had to put in on the vehicle.

My delema is this, on monday morning when i dropped off the car, the guy david is the manager of the shop and he quoted me
$438 + maybe $75-$100 dollars for the samco hoses. So i agreed and he drew up a legitiment reciept and we both signed it.
I am now starting to fear that they may seek to charge me more for labor and i am for certain that i wont have to pay more than what he originaly quoted me and we agreed upon. So my question is, do they have the right to change their price even after they gave me a final quote in which we both agreed upon and signed for? Im just wondering if i go to pick up my car and they try and charge me double the price if i have to pay them that or can i argue the fact that they were the ones who set the price before fully realizing that they were going to have to put in more work and hours into this car?

I feel like they won't be able to charge me more than what we agreed upon, based on their poor judgement on the amount of work they were going to have to do to finish the job. And i don't feel like i should have to pay more money based on their mistake, is this true? or am i at the mercy their rules?