Jorn...as Mike and Bruce have indicated, if a GC is not in the competitive bid business, they're most likely negotiating work and using what the commercial world labels a GMP formatted agreement. Cost of the work, plus a fixed fee with a guaranteed maximum price. Most experienced GC's fix general conditions as well....field supervison, temporary utilities, etc. Savings from the GMP are split with some percentage to the GC and some to the Owner. Unforeseen conditions are identified in the agreement and it would be wise to establish unit prices and hourly rates for events such as encountering rock (define rock too), hauling away additional spoil beyond what is indicted on the site plan, importing soil, Winter conditions, adding outlets, etc. The cost of the work plus a GMP is very good format for complex projects and your architect can recommend an AIA agreement that is appropriate for your project.

With your project, you're asking for people to spend several weeks studying your documents and provide a detailed (low) budget while you, your wife and the design team have had several months to dive deep into the project. There's going to be some miscommunication of "intent" somewhere down the line and your definition of risk and your expectations for performance might not be clearly defined in the project documents. Conflict resolution needs to be quick, decisive and systematic. A well known principal from HOK once commented that on low bid projects, his architects were essentially devoting the majority of their time to practicing what he defined as "defensive architecture". The selection of a GC in your case might be the firm that is best suited to work under this format and perhaps ask your prospects to clearly outline the process that they propose in resolving conflicts and document clarifications with the design team.