Just contact your ISP to get a public IP. You might not get a static IP, but you can configure a dhcp client to request your old IP when reconnecting after a power outage. Set DNS TTL reasonably low like 12 hours so that you can recover if you do get another IP.
Another way is to signup for a cheap VPS and use a tunnel to your home server. There's lots of really cheap VPS's with 128MB of memory that is plenty if you just want a tunnel.