As @Florian answers, the short answer is that we actually need to look at the term "baseline," which is the legal term used in international treaties.
The authority for FAA jurisdiction over the airspace defined in §91.1 is given in 49 USC 40103. This is shown in the official Federal Register docket of 14 CFR 91.1 which lists all authority basis for the regulation. 49 USC 40103 states in pertinent part:
(a)Sovereignty and Public Right of Transit.—
(1)The United States Government has exclusive sovereignty of airspace of the United States.
For the purposes of this code, the legal term "United States" is previously defined in 49 USC 40102 as:
(46)“United States” means the States of the United States, the District of Columbia, and the territories and possessions of the United States, including the territorial sea and the overlying airspace.
So to understand what the FAA actually has jurisdiction over, we actually need to understand what the term "territorial sea" means, so we know what the FAA meant by "coast."
In 1988 US president Ronald Reagan issued proclamation 5928 which declared that the US is sovereign over the territorial seas and defines this as the area extending 12 NM from the baselines of the United States.
This NOAA page defines the baselines as the low-tide line of water along the coast as charted on certain NOAA maps. That page also defines "territorial seas" as waters that extend seaward from the baseline up to 12 NM. I think water past that would be international waters with freedom of passage for any nationality. More specific to this discussion, that same page defines a separate term, "internal waters", as opposed to "territorial seas" :
Internal waters are the waters on the landward side of the baseline from which the breadth of the territorial sea is measured. Each coastal State has full sovereignty over its internal waters as if they were part of its land territory. The right of innocent passage does not apply in internal waters. Examples of internal waters include bays, rivers and even lakes that are connected to the sea, e.g., the Great Lakes.
So based on the NOAA sources, the Great Lakes are specifically excluded from Territorial Seas for this purpose, and by extension, for FAA purposes since the FAA authority is derived from the same basis.
In the absence of a specific FAA provided definition, these combined facts are probably the best answer to this question.