Getting the Franks to accept Arian instead of Nicene Christianity (and move Arianism from a Gothic-only club to a translate-Bible-into-every-native-language-club) and you're half-way there.
1) Eastern Germans converted to arianism OTL because it was part of the Arian or Arian-favoring emperors.
It was accepted by their rulers because it gave them not only a good religious base on which make support their legitimacy (the king being associated to Christ, subordinate but more or less equal to God) but because it allowed them as well to be more accepted by Rome.
2) Why did Franks never were converted to Arianism? Less unified (a collection of tribal kings), already in the favors of Romans (being relative sure allies in this region), and finally support from Arian emperors ceased, short of Arian emperors.
3) When Colvis strengthened his power, Arianism was pretty much a non-option : it would have meant a submission over Theodoric's dominion, a certain clash with local elites (essentially, to not say entirely, orthodox) that even when he was pagan saw him in a good light (mostly because he WASN'T arian).
4) Why Arianism was a german-only club? It was theorically such because germanic kings wanted to preserve the distinction between german and roman elites : preventing the appearance of a merged romano-german nobility, having the possibility to lower the roman elites (that were, in urban places, mostly religious ones as bishops), and to maintain the distinction in order to, perhaps, keep the german elites as the bulk of armed forces (fearing that a romanisation would make them lost that).
Even with supporting it as they could, they failed.
Because whatever they wanted, they couldn't prevent the effective merging of population (it's one of the reasons Franks managed to dominate, they didn't cared too much about this merge happening) and the conversion to orthodoxy (while roman conversion to Arianism are almost unheard of)
Basically : Roman Orthodoxy was attractive, as it represented a will to put roots on the country and allowed wider alliances. Gothic Arianism wasn't because it maintained a less and less desirable separation and increased the risks of clashs.
Also, isn't the Gothic alphabet more derivative of the Greek one?
Being not greek, whatever in script or language, or latin or hebrew, is enough to consider its use in a liturgic manner as heterodoxial.