This must be exhausting and driving you mad. My DC4 aged 12 months wants cuddling all the time at the moment which is lovely in a lot of ways but not eg when you're trying to wash the dishes etc. Anyway .. enough about me ..!
Playing devil's advocate here - could it be that you feel resentful towards him (I would TBH)? Hel'll probably pick up on this from you facial expressions and body language (this advice is as much for me, I'm realising!)
YOu've probably tried this already but perhaps you could be the one who instigates the cuddles as it might be that this will make him feel more secure and less in need of battling for your attention. I appreciate that this is probably the last thing you to do but it's worth a try.
What about trying group hugs with you and his siblings, or sometimes, if you are holding hands with DP asking him to hold hands in between you and/or giving him a cuddle.
I don't know if any of this will help, or if you've tried it before. Maybe he'll be less of a "possessive little git" if he feels less pushed out. I'm not suggesting your behaviour is actively pushing him out, but who knows what goes on in the mind of a 15 month old?
How old are his siblings? If they are old enough you could explain to them that you know his behaviour is unacceptable, and that you need their help to try to fix it ... Eg -next time I'm having a cuddle and DS2 wants to join can we say "Come on..come and have a cuddle with us...". COuld they also try cuddling him at spontaneous times when you're not in on the act and he's calm and happy?
Could it be that his siblings are really good pals and play together a lot and he feels left out and therefore resentful towards them? 15 month olds are often pretty annoying to their elder siblings, but it must also be a frustrating age for him - not being able to express himself but wanting to communicate...wanting to join in sibling games but not quite old enough to play some of them...
I hope things get better. In the meantime I'll try not to roll my eyes when my 1 year old wants yet another cuddle the second after I've put her down so that I can do something with two hands!
It will get easier...it will get easier..it will get easier!! 