Pronounce like a Native Japanese

I have watched a youtube video on 'how to talk to Japanese people' and the main message was that Japanese respond to good pronunciation rather than the knowledge of lots of vocabulary. Is this true? I also watch a video where this guy goes over how to pronounce different consonants.
In a couple weeks from now I have to give a speech and I want to sound as "fluent" as possible. I haven't been studying Japanese for that long so I still have the 'American accent' and I want to get rid of it ASAP .
Does anybody have any tips on having good pronunciation (excluding shadow reading)?

Japanese respond to good pronunciation rather than the knowledge of lots of vocabulary.

I don't quite think so. Really heavily accent of course makes it difficult to understand exactly what is being said, but that is about it.

I don't know what kind of "American accent" you have, and how long you have been learning the language, but if you don't have an opportunity to listen to Japanese being spoken by native speakers, try to pronounce the vowels as in Spanish, the "a, e, i, o, u" are similar to those in Japanese. The vowels pronounced in a typical American way can stand out - if each "a" sound in "watashi wa Jimin desu" ("I am Jimin") is pronounced like "a" in the word "hat," that would stand out as not yet having mastered the basic pronunciation.

Does anybody know if there are any speech therapists in Japan who can teach gaijin a good Japanese
pronunciation?

I believe all teachers of the Japanese language have been trained in phonetics as part of their training course, so they should be able to give you some tips on pronunciation as well (though whether they are able to explain in English might be another question).

I don't know which video you saw, but I do think it's universal that people respond better to "plain speaking" such as plain English, plain Japanese and so on.

If you're American (and old) you might remember "the Professor" from the TV show Gilligan's Island. He would always use many difficult words and talk long only to puzzle those trying to listen to him. Simple is always best.

At the same time, I don't really think that "native pronunciation" is always required. It's just that "bad pronunciation" is difficult to comprehend whatever language you're speaking in.

You say you are giving a speech. Try to use short and simple sentences rather than to show off your structure and layers. As for pronunciation, why not just try to talk slowly so that you can pronounce each word "as properly as your knowledge wishes to"? Another key is that the romaji R should be pronounced more like an L.

In any case, smart people are those who can make difficult things sound easy. And in fact, I think that's what fluency is too.