We did a nap 3ish for 20 mins with a 7pm bedtime no trouble when we hit the nap-dropping phase. I know you say it's not worth the bother for such a short nap but my feeling would be if it stops you all being up all night until he can really cope with no nap, it's worth it! You don't even have to really 'try', just invent a reason to drive somewhere at 2.30/3ish and give him 20 mins from when he dozes off. If he doesn't just do a bit early bedtime. Honestly it won't last long, 2-3 weeks of doing this every other day or so and we were pretty much done x