Been there, done that.
Ice melt lines — as well as pipeline heat trace tape — leak some current as part of their design. That’s why the instructions specify both a maximum length as well as using THEIR ground fault protectors. IIRC, the “special” protectors trip at about double the level of ordinary GFCI’s.
This gives you two choices: either hard-wire the cables or restrict their length to about half the allowed length.
NEC is deficient on this point. While there exist GFCI breakers set at “equipment protection” limits, code makes no provision for receptacles protected at this higher limit. This means trouble for ice melting lines on the roof as well as for heat tape for n the crawl space.
Code does allow for use of these higher fault limited circuits for machinery, but leaves mandated receptacle limits alone.
