The Arabic phrase translated as "the good things that We have provided you with"...
The Arabic phrase translated as "the good things that We have provided you with", would be literally translated as 'the good things of what We have provided you with' - in genitive case. Apparently the adjective (the good things) is the first construct, related to the second construct (what We have provided you with); and means in effect, 'eat from Our sustenance that is all good'.
This meaning is appropriate in this context which is meant to show Allah's kindness and compassion for the believers. The phrase is not meant to restrict the second construct with the first one.
In other words, it does not mean, 'eat from the good provisions, not from the bad ones'; because such meaning would be quite irrelevant in this setting in which Allah wishes to remove prohibition, telling them not to abstain from any provision given by Allah - as, such behavior would be a self-imposed unauthorized legislation, would be a talk without knowledge.
QUR’AN: and give thanks to Allah if Him it is that you worship: Apparently it should have been 'give thanks to Us', but the Qur’an says, "give thanks to Allah". This expression is more appropriate for the theme of monotheism which the verse leads to. And for the same reason the next phrase, "if Him it is that you worship", was preferred to a shorter, 'if you worship Him'. The present expression restricts and confines the worship to Allah alone.
QUR'AN: He has only forbidden you what dies of itself, and blood, and flesh of swine, and that over which any other (name) than (that of) Allah has, been invoked: Invoking any name other than Allah's, means slaughtering for any thing other than Allah, for example, sacrificing for idols. QUR'AN: But whoever is forced (to it), not revolting, nor exceeding the limit: That is, when he is not unjust, nor does he exceed the limit; is driven to it because of emergency.
The meaning is therefore as follows: Whoever is forced to eat some of these forbidden things, because of some emergency, while he does not like at all to go against the law of Allah, nor does he exceed the limit, there shall be no blame on him. But if he was trapped into that emergency because of his own revolting behavior or because he had exceeded the limit and was then driven to that necessity, then he is not allowed to eat from these things.