I don't think this is an improvement to this entry - I think it's based on a misunderstanding of how the expression is actually used - and I think spreading out the arguments for changing these closely related entries over both of them makes things very confusing.

see comments at new xref.

daijs:
知らん顔をして問題にしない。不都合なことには触れずにおく。「自分のことは―・げて人の悪口ばかり言う」

I actually wanted to give:
　to act as if (something inconvenient to one's argument) is not an issue
But that's quite the parenthetical. Not sure what the best gloss might be(or what is technically the most correct). Whatever you might pick, I just don't want to encourage the use of this verb in a generic way, when it is not at all generic.  (ie. it doesn't mean "to ignore (something)".). 
彼女を棚に上げ	0
宿題を棚に上げ	0
ニュースを棚に上げた	0

I tried 責任, and got some hits, but they were remarkable structures using "みずからによる":
責任を棚に上げた	103
みずからによる責任を棚に上げたような印象を残した
自分たちの責任を棚に上げた悪態であるが

etc.

If you do a book search for 棚に上げる, you'll find a preponderance of 自分の事, followed by distantly by some variants like 自分の問題:

自分の事を棚	6673	97.6%
自分の欠点を棚	108	1.6%
自分の問題を棚	57	0.8%

You can find references to specific points of argument, as in "well, then I'll just ignore XXX event if you're going to ignore YYY event".

@@ -15,0 +16,2 @@
+<pos>&vt;</pos>
+<xref type="see" seq="2858678">自分の事は棚に上げる</xref>
@@ -17,2 +19,2 @@
-<gloss>to be blind to one's shortcomings</gloss>
-<gloss>to play innocent</gloss>
+<s_inf>esp. 自分の事は/を～</s_inf>
+<gloss>to act as if (something inconvenient) is not an issue</gloss>

@@ -5,0 +6,3 @@
+</k_ele>
+<k_ele>
+<keb>棚にあげる</keb>

@@ -12,0 +13 @@
+<misc>&id;</misc>