Advice Needed: Sippy Cup Training

So, here's item 473 on my list of parenting-related things to obsess about: how to make the transition from bottle to cup.  The little one has never taken to a sippy cup, really, always preferring a good old bottle instead.  My pedi says we really don't need to stress about this, despite the American Academy of Pediatrics' recommendation that babies are weaned from bottles at 1 year. Still, I figure we should begin the gentle transition now that he is just about 13 months old.  So... I recently purchased some Born Free training cups and spouts (happily BPA-free) at a friend's suggestion.  The problem is, although he hasn't refused it outright, I'm concerned he's not getting enough to drink when we use it, because the spout is sort of funky and doesn't allow a free flow of liquid as a result of the usual sucking method.  Instead, you sort of have to bite on the spout to get the liquid out and then swallow it.  I guess in this way, it helps the child learn how to drink rather than suck.  And yes, I only know all this stuff because I tried it myself!  Anyway... it took him nearly 30 minutes to drink only 1 1/2 oz. of milk before bedtime last night, whereas with a normal nipple/bottle it only takes him about 10-15 minutes to drink about 4 oz. So... the question... is it OK for me to give him a bottle/nipple at times when he is really hungry, like first thing in the morning, and then use the training spouts during the day when the "need" for the bottle is not so urgent?  Or will it confuse him not to be consistent with the training cup?  Experienced mothers of the world, please weigh in... I'm desperate and paranoid that I am going to starve my child!