In my opinion silver is just for werewolfs.
Silver is considered a pure metal, which makes it very effective against many kinds of supernatural forces. For the most part though, silver only had the ability to restrict the movements of a vampire or strip it of its powers. It didn't become fatal until more recently, with works like
The Lost Boys (1987 movie) and
Hellsing (manga series), along with the short-lived drama series
Moonlight giving it a slow killing, kryptonite-like quality. Additionally,
The Strain Trilogy follows the idea that a stake only works if it's made of silver.
And in some myth they can't pass running water.
That's also true in some cases, though North American and European folklore say it doesn't affect them at all. The latter does, however, state drowning is fatal to a vampire, and in the original
Dracula, even the Count himself could be killed by drowning.
Like I said, it depends greatly on the source material. I could rant forever on the differences, especially now that the creature's sexual undertones are being substituted for romantic overtones. The very least I'll say is that some stories don't even require it be through the heart. In some stories is the stake is used only to open the chest, while others went for the mouth, and still others the stomach.
I'm not even sure if the traditional wooden stake and mallet combo in vampire movies is enough
It depends on the hammer in question. A heavy head with that perfect handle length can deliver enough force on the necessary area to drive the stake, and it does help if the stake is made of a dense wood or silver. If all of this is factored into the equation with our protagonist's strength, and it could help to have gravity aid the drive, then the hardest part becomes the initial drive, when the stake has to break the skin. Furthermore, there is a vulnerability in the human body concerning the heart. If struck, even a fist can deliver enough enough impact to a heart and stun the victim completely. It's the same location doctors and paramedics attempt to strike when they need to inject a needle into the heart - precisely because it bypasses most of the defenses. The main drawback is it's tiny, barely larger than the circumference of a finger, and is made even smaller when approached head on; for this reason, striking from above is preferred in both cases.
Beeble, it's tricky, but we've laid out your best options:
Injection-style staking.
Drowning.
Bludgeoning or stabbing by silver.
Decapitation with a car and wire.
For the last one, think outside the box a little. This is merely a suggestion, but a simple approach is to use the afterglow to your advantage.