Newborns mean always having to say you're sorry (but not really)

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I thought about starting this post off with the obligatory apology for going so absolutely silent. But I do a lot of apologizing these days and felt like my own blog was the one place where perhaps I would skip that step. With the baby and everything else going on, I've dropped the ball on many things - mostly things other people want me to do for them. Most of my apologies are partially heart felt. After all, I am sorry that I (fill in blank with thing that someone else thought was important but I didn't do here). However, it's not like I've been eating bonbons and sipping pastis so I'm only sorry they're unhappy with me; I'm not sorry that I didn't do what they wanted. So I write a lot of emails that have various of the elements below:

Dear important-person-So-and-So: I am so sorry that I haven't responded to you in several months. I know you thought your (fill in blank here) was incredibly important but over the past few months I have: 1) Had a baby, 2) see #1, 3) went through the tenure process which required putting together my tenure packet and giving a talk while operating on only a couple hours of sleep and nursing a newborn and I only had two hours a day to get stuff done because my baby hates napping, 4) see 1 and 2, 5) tried to keep my research program rolling by writing an assload of grants to funding agencies with apparently negative funding rates (I didn't know negative funding rates were possible either, but there you have it) and finally, you guessed it, see 1), 2) and 4). Much of my work time these days is spent holding a baby with one hand, typing  with the other "obviously, the predictions of the model are well supported by..." while blowing raspberries and saying such erudite things as "roly moly poly foly toly" (she apparently loves rhyming nonsense).  As you might now begin to suspect, my email inbox looks like someone sent it a Howler which did a lot of screaming and then exploded. Terribly sorry. Hugs and Kisses, Professor Chaos.

P.S. please don't respond to this email unless its really important as it will take me another few months to respond. In the meantime seeing your unanswered email in my inbox will cause me great guilt and anxiety which, contrary to all logic, will not actually make me respond more quickly but will only make me not respond to more emails until your email spills on to page 2 of my inbox and I no longer have to look at it (and thus no longer feel guilty).

I once tried to email an important but absentminded professor who apparently had allowed his inbox to fill to its quota and thus bounced back incoming email. I'm beginning to think it was not absent-minded at all but the most brilliant strategy known to man...