"Unless the ice had already stretched from the unspecified part of his back and covered his shoulder blades, I think he'd be able to at least reach back, if not do the throw."

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The problem is not the reaching, it's that, in order to move the Champion, he'd have to break the ice covering said unspecified part of his back.. Because said ice is affixing the Champion to Fangir there. Literally the strongest part of the ice must be broken, with a one handed over the head pull (not the body's strongest maneuver).

I don't think* a normal person can perform a throw with one hand like that (given that the Champion is set and has no momentum for Fangir to use against him), and given that the magical boosts to strength and magical boosts to "stay there because ice" are equal, I think it'd just be a painful tug.

*by no means a martial arts expert, but the judo throws I have seen all involve two hands. and generally having an extended arm or forward momentum.