[[*gʰeud-]]
Please give the sources then. I'd like to check them as far as I'm able. More descendants would also help.
I am not able to add links with the idiosyncratic way you have your talk page set up, though I have tried again and again to do so. On Google Books, the source "Encyclopedia of Indo-European Culture" by Douglas Q. Adams contains "*gudóm" (intestine) as well as "*gut-r" meaning "throat," "*gutr" meaning "gullet, and other related terms. "*gheu" is given as meaning "pour." They seem like completely different words. I do recommend our re-examining the assignation of "*gheu" to the etymology of gut pending the creation of gudóm.
Pokorny says "gut" comes from *ǵhewd; see http://indo-european.info/pokorny-etymological-dictionary/whnjs.htm.
Sorry, the proper link is http://indo-european.info/pokorny-etymological-dictionary/%C4%9Dheu.htm. You can include links by just pasting the raw link, without adding brackets or anything.
The gullet entry gives *gʷel- (which we also don't have an entry for) as PIE root.
I agree with CodeCat here about sources. From what you've said, the Adams book doesn't appear to say that "gut" is derived from *gudom; the sources should explicitly make the link. What does Pokorny say, for example? PIE *g -> Germanic *g is unexpected. gut vs. gudom could be a coincidence (cf. have vs. Latin habēre). Note also that etymonline agrees with the derivation from *gheud (although this is not a primary source).
The relevant page in the Oxford book seems to be this, which gives a Low German reflex that starts with a k