When we eventually get our three day old baby to sleep after what seems like hours of pinkie time and rocking, within five minutes of putting him down his violent arm and leg twitches cause him to wake and start fussing again. We've tried swaddling, to no avail, and we're definitely waiting until he's properly asleep (ragdoll for 15-20 minutes). Is this normal?! Any strategies for mitigation?
First, yes, this is normal. Getting infants to sleep is one of the most common (and distressing) problems parents face, and it is very significant in the manner it influences parents. But it never hurts to give your pediatrician a call; they can ask you more questions than we can.
Newborns have a number of very important reflexes, which vary in strength depending on their sex, physical and gestational maturity, state of arousal (sleep stage), degree of motion, and many other factors. That awful arm and leg 'twitch' (where they throw out their arms and their legs extend) is called the Moro Reflex - or startle response - and it is disturbing to the infant, who feels that he is falling. That's why he cries when he feels that, and why he usually settles down quickly with a snuggle.
Swaddling has been shown in studies to decrease the number of startle responses and the progression to full arousal in newborn sleep. If you are swaddling correctly (please read about safe swaddling), you can try adding motion (that's why the old baby cradles were on rockers.) Your newborn is used to sleeping on the go (mom was often moving while he was napping). This post addresses this nicely.
Swaddling, movement, and noise (the right kind - that which simulates the swooshing sound the baby heard in utero) all have been shown to help most newborns to sleep.
If all else fails, please know that unsettled sleep behavior (as well as crying) in infants is commonly a transient phenomenon that peaks at 6-8 weeks of age and is much diminished or gone by 12 weeks.
Using the search function on this site (e.g. newborn, sleep will bring up many good posts; same with crying newborn, etc.) You might be interested in this post on picking babies up each time they cry as well.
REFLEXES AND THEIR RELATIONSHIP TO BEHAVIOURAL STATE IN THE NEWBORN
Neonatal startles, smiles, erections, and reflex sucks as related to state, sex, and individuality
Spontaneous Arousals in Supine Infants While Swaddled and Unswaddled During Rapid Eye Movement and Quiet Sleep
Distinguishing infant prolonged crying from sleep-waking problems
Infant crying and sleep research
If swaddling isn't working for you, try one of several different types of blankets with built-in swaddle arms/velcro/etc.
I found out shortly after coming home from the hospital that both of us are terrible at proper swaddling. We bought a sleep blanket with built in swaddle arms that velcro in place. Our daughter was sleeping through the night (8+ hours) at about 1 month old, and I credit the blankets for that.