This information may be useful for future reference:
We had two home laptops set up in our flat both with six different browsers refreshing about once a second. My flatmate's laptop got through after five minutes with Opera (I think it has an inbuilt VPN). My laptop didn't move from the holding page on any of the six browsers being refreshed once a second for 55 minutes until at the very last Firefox got through (no VPN). Tickets were purchased at 9:57am, a minute before the sell out announcement.
It was feeling like there was no chance I was getting through from the holding page and then it happened after 55 minutes and what must have been 20,000+ previous refreshes across all the browsers.
I also had a work laptop with three browsers refreshing every second and four browsers refreshing every 20 seconds over phones and tablets also on the case too and none of them got through.
I think this suggests that it's unlikely you can saturate requests from using multiple laptops / browsers even refreshing them all more or less at once (although no individual browser would have refreshed more often than once a second) across two different laptops on the same IP address.
It also suggests that you should keep persevering until the bitter end as it looked like there was no hope until all of a sudden there was.