Actually, Treccani only gives svelgo as an alternative form for just the 1st person.
DOP, as you say, gives as basic conjugation the one with svello (implying svelli, svelle etc.) while svelgo, svelgi is denoted “meno com.” (= “less usual”). So, both Treccani and DOP agree on svello, svelli as the main conjugation.
Zingarelli too gives this as the main form, while giving, for the 1st singular and 3rd plural persons, also alternative forms svelgo and svelgono as “disusato” (= “no more in use”). The Grande Dizionario della Lingua Italiana refers to divellere for the conjugation, and for the latter verb simply gives both divello and divelgo.
All in all, the normal conjugation is svello, svelli, svelle etc., while some forms of the conjugation with “g” have appeared somewhere, sometime, but are less usual.