Catnapping, sling loving little one

[Monkeyboy1]

Help. I need some sage advice. My 7 week old son is a confirmed catnapper (from 2 weeks of age), wakes at the 30-45m mark no matter where he sleeps, and screams. In the sling I can tide him over and he will go another 1-2 sleep cycles but in the cot/car/buggy there is no chance and that's it he's awake, tired, miserable and it's all downhill from there. Timing of feeds goes out the window, as does any hope of getting anything done. Inevitably he is horrendously colicky in the evening and cries/screams non stop for anything up to 5hrs unless he is put to sleep on my chest or his front in the cot (I know this is wrong but I'm desperate). I should be battle hardened as my daughter was exactly the same (now 27m) but to be honest I am devastated Lightning has struck twice. Every day is a new level of exhaustion as I can't put him down, with the added difficulty of my toddlers jealousy because the baby is constantly strapped to me. Every time I try to get him to sleep somewhere else it is agony for all concerned. At night he will eventually go a few hours in his bed (this is a new development thank god) but in the day no chance. I know it is normal for babies to want to be held so my question is this... Do I just give up trying to get him to sleep elsewhere until the "magic" 12 week mark? Or should I keep trying? I am worried about making a rod for my own back and him not being able to settle elsewhere ever. When is it considered "ok" to start leaving them to cry a bit? With our daughter it was all so distressing I am horrified at the thought of sleep training all over again, but my back and my sanity can't cope with months and months of never being able to put my baby down. He is otherwise well, exclusively BF and growing and developing normally.