Newborns sleep up to 16 hours per day and they wake every 4-6 hours so in that stage, their circadian rythyms never seem to be the same as adults.  (Which is always a pain--- :) )  Howevrr, as the baby starts to sleep through, I would imagine that their circadian rythyms do come more into line with an adults or a childs.  of course they still have their sleeps in the afternoon often, but then this is reflected by the smaller dose in the afternoon anyway.  It is therefore the late night dose again that is a problem.  To give or not to give.  Personally, the only thing  that you could do is try the routine and see how it went.  If there was a patch where baby woke and was fully alert at 3am and you were unable to go back to sleep, I would imagine that it was best to slip back to conventional dosing for a little while longer. 

Tips for dosing at this time (3am) and doing this with as little stimulus as possible would be to keep the room dark where the child is and carry a torch.  I have to have a small pen torch to go dose Ashley as the slightest light in the house wakes my youngest and we then get not only the birds cheaping but him calling out.  So obviously our door is shut when our alarm goes off so that it does not disturb him and then we creep (fix all the squeaky doors and floor boards as I can assure you---that squeak WILL wake the child---LOL) and use the torch so we don’t break necks doing it.  Oh and whilst we are on that topic....  make sure there are no toys lying around in the way from A to B cos that is a hazard and also a potential baby waker also.  When you actually dose the med’s, have it in a syringe and at room temp rather than straight from the fridge.  Take it out before you fo to bed and let it stand.  Take it with you and have it on the bedside so your not fumbling around for it.  If the child starts to wake and chatter, just calmly tell them it isn’t waking time yet and to go back to sleep.  If they cry I have in the past left my child and they usually go back to sleep.  It is kind of like getting them into any other routine like where nighttime feeding is concerned.  Making it quiet and calm and not encouraging anything that may lead them to believe it is ok to wake up and play.  Eventually they do settle into routines like this and it is a case of being firm as you will know. 

If NONE of that works, and you are not getting back to sleep after the dosing, then you can always switch back to conventional dosing for a while longer and try again in three months or six months time.  I would imagine if you treat it like potty training (in the sense that if it doesn’t work--leave it a while and then try again later on), you will not go far wrong.