So, I understand the first sentence, but I'm a little confused about the second one.
My translation is: to have a feeling about a certain matter to the extent of being able to declare about it.
Isn't this an excerpt of a dictionary definition, like what this blog cites?
In this case, it means:
what one thinks/feels about a certain matter (which has taken shape enough to be expressed/presented/published)
As you have correctly translated, 程度 means "(to) the extent/degree", or you could take Vできる程度 altogether as "enough to V". Anyway, both ～程度 and ～程度に stands for the adverbial phrase "to the degree", but the form with に is preferred when describing the state how the result is, while without に the manner how the action is done.
30cm程度切る cut (off) 30cm
30cm程度に切る cut into 30cm pieces or trim into 30cm long
The simple answer: the に in 発表できる程度にまとまったもの allows the adverb of degree 程度(extent) to modify まとまった.
発表できる程度 translates to "the extent it can be presented".
まとまる in this context translates to "to come together; to cohere".
In order to say that ある事柄について感じた事 has まとまった to 発表できる程度, we use に.
becomes, in English:
(The substance of) what you felt about a certain matter (that has become coherent enough to be able to be presented (outwardly)).