Not having refined the issue, I rested, for some time, satisfied with an explanation that [ʧ] in the word in question is due to **t+*j (+-ī- as verb theme). But today, this word drew my attention once again, and I noticed that this is untrue for Moravian (as well as for Lechitic) languages.
I had been associating the verb with the ComSlav. lexeme -stat- (←*sta-t-), like ComSlav. *(do)statuk (especially with this word current in Moravian languages), *stati, *(ne)statia. For the Moravian languages, it could result only in +[ʦ], sta[ʦ]it(j), which is not the case here. An analogy through conjugation forms doesn’t fix anything here, cf. Proto-Czech */xətjy/ > ModernCz /xʦi/ ‘I want’, moreover, even durative or imperfect forms still preserve [ʦ], cf. sotit(j) : *satjat(j)→satsat(j). Though, even assumed some kind of ‘reaccretion’, say sta[ʦ]+it-, i.e. not from the Proto-Moravian language time, but later when the [ʦ] phoneme’s already established – this would’ve been also unlikely as far as hardly any such instance is found elsewhere in Moravian languages.
The ComSlav. root *sta- (:*sto-) is known coupled with the other diverse suffixes, as well, such as: -n-: ComSl. *stan, -v-: ComSl. *stav, -l(i)-: EastSl. *dostali, and the *sto- root is known also with the -g- suffix, as in ComSl. *stog (aside different versions thereon).
Now, provisionally I’m wondering whether it couldn’t be *-k- in this word.
NB:
1) ** (two asterisks) means the reconstructed form is highly questionable.
2) + (superscript "+") means a void form.
3) i, u mean ComSl. reduced vowels; the Moravian (Czech, Slovack) words are rendered through the phonemic transcription.