So my question: Would using a VPN and swapping out configuration files that change your IP address mask the same as using different VMs?
They protects against different things. VPN protects you from network fingerprinting, while single-use VM protects you from desktop/browser fingerprinting. To be truly anonymous you may need to use both (among other things), depending on your threat model.
If you want to/are fine with establishing anonymous identity (i.e. others can establish multiple related acts are done by the same person, but they can't track it back to you as a person), then you may be fine with just using a VPN, and but hashing to replace VMs.
But if you want to prevent people from linking your actions together, then you may need both.
VPNs have generally gateways that allow them to change the IP address of the computers connected to them. This makes it difficult to identify the computers connected to the VPN or locate them by your internet provider.
Using VMs is less evident because even if protect you mainly from browser finger printing, but you will be vulnerable to connexion log localisation, and if you use bridged mode for your VMs it is likely you disclose some private information if your VM is compromised. Also there are viruses that can break the poor security of your VM and access your host machine. There is also possibility for a spyware installed on your VM to retrieve the MAC address of your host machine.
Definitely VPNs are safer to use than VMs but it costs more, as you know, to use a VPN.