Nice find, Anna!
Let me help you with those transliterations.
First of all, any time you see a "tsu" that looks smaller than a regular character, that little "tsu" is not read as "tsu", it becomes something known as a glottal stop. It's sort of like a pause before the next letter.
English
sort of has glottal stops, and I'm trying to think of one to help you understand what I mean... we don't really realize we're doing it, but let me try anyway.
You know how sometimes instead of pronouncing a final 't', you just sort of stop your breath in your throat? You don't always say, "cat" or "but", you say, "ca*", or "bu*".
So when you see a little "tsu", you do a little stop like that. That's why "Tamagotchi" is written in Japanese, "ta ma go (little tsu) chi)": because it's pronounced "Tamago*chi".
You know what? This is too hard, I'm going to do a video of this instead. Give me a few minutes to work on that.
So all the times you have a "tsu" before "chi" in your character names, you really mean a glottal stop.
Update The video is just uploading now, and while I wait I thought of a few better examples of a glottal stop.
You know how in Cockney English, they don't say "Britain", they say, "Bri'in"? That's a glottal stop.
This video that's uploading... it's twelve minutes of me fumbling around my mom's office coming up with overly long explanations for everything.

I hope it does some good to somebody. It also demonstrated quite painfully how out of practice I am with reading Japanese. Yikes.
So here are my corrections aside from removing all the little tsus:
Babamametsuchi -> Papamametchi (that's a circle diacritic, not the two dashes)
Mama-mametsuchi -> Mamametchi (inserted an extra character there, eh?

)
Memebabatsuchi -> Memepapatchi (circle not dashes)
Kuchibatsuchi -> Kuchipatchi as usual (circle not dashes)
Chibibatsuchi -> Chibipatchi
Bababatsuchi -> Papapatchi (are you sensing a pattern yet?

)
Mamabatsuchi -> Mamapatchi
Kisatsuchi -> Kizatchi (dashes make "sa" into "za")
Babakisatsuchi -> Papakizatchi
Mamakisatsuchi -> Mamafurawatchi (thought they were all the same eh? Tricksy they are)
Hanataresotsu-chi -> Hanatarezotchi (dashes make "so" into "zo")
Bokugatatsuchi -> Okugatatchi (that first character is an "o", is there some good reason you changed it into "bo"? Am I crazy? It's an "o" right?")
It's taking forever for Google to upload this video so I'll re-update with the link when it posts.