@Gizzymum and @TheGrumpySquirrel - sorry for having been useless at replying.
My coping strategies for sleep deprivation are definitely that, and not strategies to thrive... but my DC1 was also towards the extreme end of the scale in refusing to sleep.
The advice that you sleep when baby sleeps is sterling.
Except if your baby's eyes will pop open the second you try to lay them down. Mine would only sleep in our arms for weeks, probably months. I myself am not very good at sleeping while sitting up, not to mention it may not have been terribly safe for the baby. The only practical thing to do in that situation was to have someone who would take over the baby and have it sleep on them while I got horizontal for a bit in another room (partner, grandparents...)
There are gentle sleep training techniques (e.g. those described in Pantley's No Cry Sleep Solution) but a) your baby needs to be a certain age for them and b) they are not guaranteed to work.
What kept my sanity, more or less, was firstly, understanding what is going on with the baby. That they are not doing it to be unreasonable or to manipulate you or whatever. That sleeping is a developmental skill that also matures at different rates with different babies. That it really is massively unsettling to leave the environment of the womb, when that is all you have known for your entire life, for the loud, bright, sensory-overload confusion that the outside world involves, without the capacity to make sense of it, except for the one source of familiarity and comfort, which is de facto the mother (plus the kinds of sensations and rhythms that evoke life in the womb - like being rocked gently).
I found it helpful to read and follow the Wonder Weeks book, partly because it gave an insight into what is going on inside my baby, and partly because it gave me reassurance that a) what we are going through is actually normal and b) there are good periods and bad periods, and having a somewhat fixed period to look forward to when things are likely to get easier was really helpful.
I also kept experimenting with things that could possibly have explained why my baby is such an awful sleeper, like leaving foods out of my diet that the baby could possibly be allergic/sensitive to (word of advice: if you do cut out important food groups, make sure that you get your minerals and vitamins from some alternative source. My teeth did not thank me for leaving out dairy for months on end, and being casual with the calcium tablets). We went to the doctors several times, most of whom dismissed me, but in the end DC1 was also diagnosed with acid reflux. Experiencing heartburn now with this pregnancy makes me appreciate why that might have interfered with DC1's sleep! In the end the medication did not make a massive difference, but the very process of looking for solutions also meant that I did not give up hope, so it was good for my mental health in a roundabout way...
Finally, I found a series of threads on Mumsnet, from its "most sleep deprived corner", where veterans of long term sleep refusing children were posting, and having some company in this was also a relief.
Sorry for not saying anything revolutionary and I hope I did not put anyone off. I am sure that everyone reading this will have babies who sleep through the night from a really early age!! I am counting on this myself for DC2 :))