From what I've seen online, the Recom Power Engine RC-450 is made by Andyson. Not a manufacturer known for making quality PSUs. According to Guru3d the original model had 26A on the 12V rails, while realhardtechx has the second gen model having 30A on the 12V rail.
http://forums.guru3d.com/printthread.php?t=205763&pp=30
http://www.realhardtechx.com/index_archivos/Page24891.htm
The problem you are going to have is plugs. The second gen model only has a single 8pin plug. The Guru3d link doesn't have any pin info. The 270X going from memory needs two 6pin plugs. You might need to use adapters to get this to work, and I ALWAYS suggest never using adapters. Using an adapter to force a PSU to power something it wasn't designed to do isn't a good idea. In theory the second gen model can do it because a single 8pin plug can provide 150W which is the same amount of power as two 6pin plugs. The first gen model link is also from 2006 so it's super old. You shouldn't be using a 10+yo PSU.
To be honest I'd just toss that PSU and get a new one. Even a known good 80+ bronze unit can be hand ~$35.