Hmmm.... don't have a really good answer from you, but, from recollection, we went through a few really rough weeks where Katie only had 1.5 hour nap and 10.5 - 11 hours at night, and was over-tired most of the time.
It took a while before the 2 - 1 transition settled itself, but when it eventually did, Katie started taking 2 - 3 hour naps, thus bringing her total sleep time up to a similar level than it was before.
I think this is quite common and you have to trust your instincts whilst going through this time as to whether to offer 1 or 2 naps a day. It might be an idea to cut the 20 min nap in the morning by 1 or 2 minutes at a time till it is down to, say, 10 minutes; once that is consistent, then try and cut this nap out altogether, or something like that. Or, you could just cut that first nap down to 10 mins straight away on any 2 nap day. Just be reducing that 20 min nap to a 10 min nap might mean she will go for her second nap at a time that is more akin to a 1 nap day, thus helping the transition along a bit.
I have no idea if any of what I have said is useful at all, but you will get through it eventually! (I guess the answer to your question is, they don't handle it without getting overtired, but they eventually are able to stretch their 5 hour A time to 5.5 hours consistently!).
xx
