What you want just isn't possible on a small scale.
IP Addresses are purchased in blocks by companies with a hell of a lot of money and more importantly, infrastructure. When you get one, unless you are going direct to your RIR (Regional Internet Registry), you are only renting the IP.
Even if you then owned an IP by going direct to your RIR (which can be very expensive just to register... See ARIN, RIPE), I highly doubt any VPS provider will host your IP/BGP/AS as it will require a significant change to their own infrastructure.
The best thing you can do is to use a single provider that specialises in uptime/100% availability, it will be expensive, but, this is by far the cheapest way of going around it.
Other solutions include looking at colocation inside a carrier-neutral data centre... but... what you are asking for is hard.