I'll reply here rather than PM, since it'll give others the chance to pitch in if they see fit.
Upgrading from any speed is always a very bad idea when there's problems beforehand, because connection problems are rarely bandwidth related and so remain unfixed, but you'll be paying more, and have a new 18 month contract start. That's doubly the case with Gig 1, because the way the technology is used is far more demanding of line quality, so a connection that works OK at 600 might not even achieve that speed when nominally upgraded to 1 Gbps - a fair few posts on this in the forum, and the company response is not always what you'd hope for when buying their flagship product.
As I see things, VM seem to have tried the "fix by replacement" tactics for your connection, and you've still got time of day related latency problems. The relatively good performance between half midnight and about 6 am suggests but does not prove over-utilisation, there can sometimes be other causes, but in view of things already tried there's fewer other explanations. At the level showing, it is possible that by VM's own undemanding criteria they wouldn't classify the area as being over-utilised, and in that case there's definitely no hope of a fix unless the problems become notably worse. It isn't just gaming that's hit by poor latency - VOIP calls, videocalls, live-streaming and Teams/Zoom applications are also affected, so if that's relevant then consider as part of the where next thinking.
If you want an Openreach connection but only for gaming, then chances are that a 35 Mbps connection would be fine - at least consider a provider with good service like Zen Internet (or Aquiss, uno, IDNet, CIX, or even AAISP) before just choosing the cheapest. Or you might want to go for a higher Openreach speed and seek to leave the VM contract. Often that requires complaints and escalation to avoid early exit penalties, but if you've just had the price increase email then you have 30 days to cancel (plus a further 30 days of the notice period) and avoid the hassle of complaints. As that's say 58 days in total if you issue the 30 days notice 28 days after getting the price increase email that should be ample time to get the new connection in place and any tidying up of emails etc sorted.
