Thanks everyone for your replies, due to the aforementioned lack of time I've managed to miss all of my notifications!
I appreciate all of your input, genuinely. To provide a bit of additional background to my situation I work 60+ hours a week running my small business and my wife is currently unable to drive for medical reasons. I'm therefore picking up the slack for getting my two children to clubs, sporting events, before and after school care as well as taking my wife to and from work. This isn't a request for sympathy you understand - I have a great life and family just pointing out that I'm not being lazy when I say I haven't got time to visit Game, check stock alerts, pop into Argos etc.
So based on all of your advice I've resolved to do the following - I'll install the Hot Stock app and monitor it for the next 3 weeks. Equally I'll try and call into Game this weekend and speak with a manager to see if that can possible bear fruit. If at the end of this I've been unsuccessful I'll swallow my pride and pay the extra to one of these unscrupulous scalpers. Thank you to the person who mentioned buying from FB marketplace. You've reassured me that these people are just grifters and not actually scammers or criminals (well, not all!)
I know that this is an extravagant gift for my son, but as a deluded parent I feel he's worth it and I over-compensate for my own childhood where my parents (whilst wonderful) couldn't afford to get me nice things.
Anyway, thanks again everyone - as previously mentioned I genuinely appreciate it.