Some ten years ago, I (a native German speaker) started learning Hungarian in an evening course and continued for roughly two years. After English, Polish and Spanish, this was my fourth foreign language.
From my personal point of view, there are some misconceptions regarding Hungarian.
The most prominent one is the "35 cases" thing. An example:
[something] of my father. This combines
apa (father) plus two possession relations into one word. Is this a "case"? I don't think so. It's just the words
of affixed to the noun, as if in
father-my-of. That's a different way of thinking, but when you get used to it, it's easier than in some indo-european languages.
What's a bit special about the suffixes, is that they take on different forms depending on the phonetics of the noun they're affixed to. The hungarian vowels come in two families:
e, i, ö, ü vs.
a, o, u, and the suffix typically uses the same vowel family as the noun.
"In Indo-European languages, there is typically only one present tense": I don't think so. Slavonic languages are indo-european, and have a clear distinction between "definite" and "indefinite" forms of verbs, Engish has the "present progressive", German often expresses the difference with prefixes. So that's nothing very special.
Pronunciation of a foreign language is always different from your native one, and at least for a German speaker, it's not too difficult.
"You have to have a complete understanding of Hungarian grammar in order to nail the precision and subtle inflection it requires to accurately convey your meaning": I never had that "complete understanding" and was able to communicate. If you know the meaning of one single suffix, you can already use it to convey that meaning, no matter how much you know about the other existing suffixes.
The Hungarian vocabulary is different from English. But it borrows many loanwords from western languages, e.g. you immediately know what a "múseum" is. But yes, when coming from English (being a romanic-germanic mixture language), you won't find as many similar words as e.g. in Spanish.
So, my overall judgment is, it's a different language, not a difficult one.