DevNTG

https://docs.moodle.org/23/en/Converting_your_MySQL_database_to_UTF8
This explains it in full, I used the commands needed from here, then you have to make sure to change all instances of the current charset to UTF8 with something like vim or nano. After that, reimport the dumped DB, and try running the upgrader again, and it shouldn't ask you to convert anymore. Your forum will go down with this change though, so I recommend that you make proper notices when doing so.
This honestly can be done for any charset of any kind, and if the converter is doing weird stuff from the beginning, I suggest you ditch it and use this instead. 

Nice-
I am sure those having trouble converting or issues with the converter itself will find that there is another alternative to getting it to play nice.

Hey can you add this guide into this please: http://reecea.github.io/ipb4-css-guide/ 

Which utf-8 version?
I found there is a problem with key-length in 3.4.x tables when you upgrade to the extended utf-8 version (utf-8 mb4?), causing significant problems in 3.4.x.
I'd suggest upgrading only a copy. Creating a copy, on a different domain, or even just a different directory, you can do by following the instructions I provided a while ago. I just found it again, here it is:
https://community.invisionpower.com/topic/408977-moving-or-copying-an-invision-community-suite-34x-installation-to-a-new-site-or-new-path/
Kind regards, Wim