Punctuation with block-quotes
Solution 1:
You can see just in this forum that sentences are not generally continued after block quotes.
However, it is explicitly stated in the MLA style guide that the sentence preceding a long quote set off by indentation should end with a colon, that the quotation should end with a period, and that the next sentence should continue at the normal indentation after the quotation.
The following shows this...
This is a block quote:
Indent this, then end the sentence with a period.
Continue afterward with another sentence.
Solution 2:
In this case I do not think it makes sense to try to continue the sentence. A quote that is long enough to be blocked and indented is one that likely has multiple sentences within it. For that reason, the reader's cognitive frame may already have changed to that of the author of the quote.
As such, it would probably be better to continue with a short recap that segues to your own thought: "Because X believes in Y, X is therefore committed to..." or something like that.
With short quotes that are less than a sentence long, feel free to include your comma. In that case you include the comma before the closing quotation mark.
Note that block quotes don't have quotation marks, and so on that grounds it also kind of makes sense that they don't accept commas linking the quotation to the main body of text.