After a couple of days of trying different tactics, I found a nice way for implementing Fizzbuzz in John Conway's #fractran in 27 Fractions.

37 1/79 1/83 1/89 606/97 89/87264 79/2727 83/3232 1/101 25123/365 39479/511 46657/803 61013/949 68191/1241 82547/1387 104081/1679 111259/2117 1/2263 3977/37 4171/41 4559/43 5141/47 5723/53 5917/59 6499/61 6887/67 7081/71 17945/73

src: https://git.sr.ht/~rabbits/fractran/tree/main/item/examples/fizzbuzz.fra
docs: https://wiki.xxiivv.com/site/fractran.html
someone else's attempt: https://gist.githubusercontent.com/malisper/7227bc8c428949d8c1f277effca28d14/raw/47935e1c9411681618da00bc786e86d8a7f96792/gistfile1.txt