Q: Does the church of Mt. 18:17 refer to the church proper or a general assembly?
A: Textually, MT. 18:17 could reference either the church proper or a general assembly, but there are several contextual reasons that lead me to understand the reference as pertaining to the church proper rather than to a general assembly: (1) the definite article preceding ekklesia denotes not a general assembly, but the assembly; (2) having introduced the concept in Mt. 16, the disciples would probably best have understood Him to mean the church proper in all subsequent references; (3) the discipline imposed would have an authoritative stamp on it (Mt. 18:18), and that authority seemingly is connected to the authority of which Jesus spoke in Mt. 16:19 (the binding and loosing), an authority not evident until the day of Pentecost (cf. Mt. 17:19-21 and Mt. 18:18); (4) the context of Mt. 18 begins and ends with the kingdom of heaven – a phrase Matthew exclusively uses (he also references the kingdom of God, but is the only Gospel writer to reference the kingdom of heaven), and which always references the 2 Sam. 7 promise to David being fulfilled on earth (God’s spiritual heavenly kingdom come to earth in physical form) – and while the ethics discussed fit the context of the kingdom, the conditions did not necessarily, but seemed instead (the conditions, that is) to reference a time when the Mt. 18:19 authority was in effect. If the “two or three” referenced there pertain to disciples only, then the conditions would fit any era in which they were functioning in such authoritative roles – and so far, the only time this has been the case is during the inauguration of the church proper. (5) If the kingdom of heaven references imply that these are only kingdom imperatives, then Christ would have prepared the disciples in a very strange way – equipping them for a kingdom which would arrive more than two-thousand years in the future, while not equipping them for the ministry immediately at hand. Finally, (6) While the disciples were not to be concerned about when the kingdom was to be restored, their authority would begin immediately (Acts 1:7-8), thus their authority was not singularly connected to the kingdom of heaven, and was very much connected to church life.
Thus, while it is not a textual necessity that the discipline scenario of Mt. 18 pertains to the church proper, the context seems strongly to indicate that as the most likely interpretation. Still, even if the text is not intended to communicate a church discipline process, applying the principles during the church age would not contradict any passage, but would rather apply a number of basic principles (i.e., plurality of witnesses, opportunity for forgiveness, consequence for rejection, etc.) in an organized manner. Hence, while I can be only 99% certain that the passage applies directly to the church proper, I have 100% confidence that the principles and process can be applied during the church age, without any tension with any other aspects of church life.
Obviously, not a comprehensive answer, but it at least provides fodder for further research.