The original construction here seems to be a conﬂation of two common possibilities. One possibility has even followed directly by a that-clause, and the other has even to followed by a gerundive phrase. There are 18 examples of the that-clause type in the original text, of which five are preceded by yea:
On the other hand, there are six examples of the second type (even to followed by a gerundive phrase); one of these examples is preceded by yea:
Related to this second type are seven occurrences of even unto followed by a gerundive phrase, as in 1 Nephi 17:48 (“even unto the consuming of my ﬂesh”).
In his editing of 1 Nephi 18:9 for the 1837 edition, Joseph Smith removed the infinitival to that preceded the that-clause. Thus he ended up creating an example of the first type—that is, a that-clause immediately following even. If Joseph had edited towards the second type, the edited text would have read something like “yea even to (the) forgetting by what power they had been brought thither”.
David Calabro has suggested (personal communication) that the reading of the original text (“even to that they did forget by what power they had been brought thither”) may be a Hebraism. In the Hebrew Bible, there are instances of the preposition fiad ‘to’ followed by ƒa¸ser ‘that’. Such examples are typically translated as until, as in this example:
In other words, the original to that in 1 Nephi 18:9 could be interpreted as meaning ‘until’—that is, “insomuch that they began to dance and to sing and to speak with much rudeness / yea even until they did forget by what power they had been brought thither”. Of course, the Book of Mormon has examples of even until. The most common type (with 38 occurrences) has even until followed by a declarative sentence without an intervening that, as in 1 Nephi 8:24: “even until they did come forth and partook of the fruit of the tree”. There is also one occurrence of even until followed by a gerundive phrase (in Ether 12:3: “even until the going down of the sun”).
The Hebrew-like construction “even to that” suggests that the original text in 1 Nephi 18:9 could be interpreted as meaning ‘even to the state that’. Despite its awkwardness and uniqueness, the earliest reading appears to be intentional and may be considered equivalent to ‘even until’ in modern English.
Summary: Restore the original preposition to in 1 Nephi 18:9 (“yea even to that they did forget by what power they had been brought thither”); the construction “even to that” appears to mean ‘even to the state that’ or ‘even until’.