Oh, wait!
There is a way to get more diamonds per diamond ore that gives you actual diamonds: you need to make yourself a factorization grinder (which involves blowing up a diamond block, among other things). The grinder will give you 2.2 diamonds per diamond ore, so it actually performs about as well as a Fortune III pick. If you blow up the diamond block, you'll also have enough shards to make an angle grinder - sort of a less-powerful Silk Touch tool that needs factorization batteries to run, but only works on most vanilla ores. Still, it's quite an upfront investment to make... not only do you need to make the diamond shards using a whole block, but you'll need a couple stacks each of silver and lead to set up - I believe the grinder needs 11 mirrors' power to run.
The grinder can also be used as part of the factorization 3x ore chain, obviously, but you can also feed it other vanilla ores, like redstone - although the yields do vary, so look it up with NEI first.