Old English did have a noun "giferness" (variously spelled) corresponding to greedy ("grædiġ" in OE), which as you say seemed to be used frequently to mean gluttony. Here's an example from the Bosworth-Toller dictionary:
Gífernys biþ ðæt se man ǽr tíman hine gereordige oððe æt his mǽle to micel þicge mid oferflówendnysse ǽtes oððe wǽtes
(greediness is a man's eating before the time, or taking too much at his meal with superfluity of meat or drink)
Old English did have a noun "giferness" (variously spelled) corresponding to greedy ("grædiġ" in OE), which as you say seemed to be used frequently to mean gluttony. Here's an example from the Bosworth-Toller dictionary:
Gífernys biþ ðæt se man ǽr tíman hine gereordige oððe æt his mǽle to micel þicge mid oferflówendnysse ǽtes oððe wǽtes
(greediness is a man's eating before the time, or taking too much at his meal with superfluity of meat or drink)
https://bosworthtoller.com/17022
And here's a sentence from Alfred's translation of Boethius that sort of links the adjective and noun:
... Tantulus sē cyning, þe on þisse weorolde unġemetlīċe grǣdiġ wæs, and him þǣr þæt ilce yfel fylġde þǣre ġīfernesse
(... King Tantalus, who in this world was excessively greedy, and there [to hell] the same sin of greediness followed him)
(Sorry, I'm just having such a great time with all this OE stuff, as you can tell)