Previous attempts have been proven unstable with varied results throughout the day – from flawless, to terrible connections.
You do need a reliable Internet connection, with no or very low packet loss. Less than 0.1% is OK, less than 1% should be still usable, more than 1% is terrible.
ping time is the most crucial element in such connections
No, a low packet loss ratio is the most crucial parameter. Round-trip time (RTT/latency) as measured by ping is the second most crucial parameter. [edit] As Austin has accurately pointed out, a low variance in latency is also crucial when working with interactive user interfaces (RDP or similar).
I have tried subscribing to a VPN service
A VPN service cannot improve the packet loss ratio and definitely increases RTT. That won’t help.
[edit] As @Bob has correctly pointed out, there are fringe cases where VPN might help: when your access ISP connection is actually good, but packet loss and latency deteriorate between your ISP and the destination network. A VPN connection might allow you to get around that problem, when the tunnel takes another route between your access ISP and the VPN provider that doesn’t hurt connectivity (as much).
However, I wouldn’t put much effort into this approach as it’s not very likely to find a suitable VPN provider without in-depth knowledge (or research) of the access ISP’s and VPN provider’s connectivities.
find out if there is tried and tested way to approach this issue
The only thing you can do is find a better Internet uplink, in respect of packet loss ratio and RTT. The latter is subject to physical limitations (speed of light mostly), so it’ll increase with growing distance (10 ms per 1000 km can be considered very good).
I am not aware on how intercontinental routing is performed and if one can direct packets through an optimal route.
That is nothing you can control, aside from choosing your Internet provider.
If connection quality regularly changes over the course of a day, you might need to adjust your working hours to that, if possible.