A Wooden Spoon is a traditional prize for the loser in a race, hence the title.
I hadn't considered the tense of the second couplet, I suppose in my train of thought, the abdication was an event in the past, whilst the advice about seeing me acting strangely was a reference to possible future events.
The "out of place" pun was happy accident :)
the jolt at the end was intended, though I can see what you mean. I had been trying to find a way of saying everyone is strange really but that not everyone embraces their own oddities.
I enjoyed your poem, and it made me chuckle. Short and simple, but with a deep message. I don't know if your brilliant play on words in the first couplet was intentional or a serendipitous accident -- I'm referring to "came in third" and "out of place." In racetrack lingo, third literally is out of place, which is second. Win, place and show. Either way, a very fun pun.
I wondered why, in the second couplet, you chose past tense "chose" rather than present tense "choose." It could be either. But after that, the poem moves into the present and then the conditional future of "If you see me..." This ("choose") could be a good place to make the transition.
Also, I did not like the last line, "What's your excuse?" Up to that point, the poem has a sweet whimsicality about it, but that line is hostile. So are the other options you considered but wisely didn't use. Of course, you may want the ending to be a jolt, or a skewering, but then the poem loses some of its whimsy, which, for me, is perhaps its chief charm. You could simply delete that line, ending with, "But I'm on leave, from London Zoo," and have a fine poem.
And the title escapes me. There must be some connection I'm not making. Wooden spoons clacking together inarticulately? If so, "Wooden Spoons" could be the title of countless poems! "A Specious Species" came to mind, or maybe something to do with hybrids? I'm sorry I don't get "Wooden Spoons."
All in all, a delightful poem to read with my morning coffee. Thank you!