You are a perfectionist! It is as close as you can get without being Russian.
I bet you I could pronounce the name "Артём" without you hearing that I am not Russian. There is absolutely no difficulty with any of those letters.
Could you make a recording please?
If there was no difficulty with soft consonants, foreigners would pronounce them correctly. Yet Germans have big problems with them. The problem is that Russian has phonemic distinction between a soft consonant and a consonant plus [j].
Russians clearly hear the difference between:
hard t + o (то)
soft t + o (тё)
hard t + j + o (тъё)
soft t + j + o (тьё)
No, my name is Johanna, so it's the first letter that is pronounced differently.
How did those people in Belorussia transliterate your name?
But I noticed that some German women who have the same name, transliterate it as Йоганна.
I think I prefer the x sound rather than the g sound as a replacement for "h".

Which option looks better to you, as native speakers of Russian, in writing?
The variant with г came from Ukrainian language, for a nothern Russian х is the closest sound, that's why they usually use x now, sometimes two variants coexist.
By the way, how true is it that "Russians can't say "H" CAN you say it, or is it really hard?
It is more than true. We do not hear the difference between our x and [h]. I can pronounce it now, but I still sometimes can't distinguish between them.
However voicing is well heard by Russians. So, a voiced h will be completely different for a Russian from an unvoiced one.