Minecraft – Is it possible to generate alpha worlds with specific seeds

Yes! And very easily, too. Profiles allow you to tell Minecraft where to store all its files by changing the Game Directory option in the profile. Just add something memorable onto the Game Directory (such as 1.7-snapshots) and that profile will never see your existing worlds.

How this works is, setting this to a different folder than the default .minecraft folder makes the game keep an almost entirely separate Minecraft install in the specified folder. (The only thing it doesn't keep separate is the game code itself – this is still drawn from the .minecraft/versions/ folder, which as you've found works just fine and doesn't compromise firewalling different installs.)

I use this myself to maintain multiple private modpacks separately from the main Minecraft version, and they co-exist perfectly and peacefully within the official launcher. It means that there is absolutely no danger of accidentally opening a modded world while running vanilla Minecraft (and thereby destroying the save!) or vice versa. I make it easy on myself by simply adding modpacks/[name-of-modpack] onto the end of the default Game Directory, which neatly stores all my modded Minecraft stuff in a "modpacks" folder within my .minecraft folder.

Your tests seem perfectly valid. If the game generates the biomes properly with seeds that have those biomes, then you're simply suffering from bad luck or you aren't looking around enough to know that your desired biomes are not available. They must be there somewhere, but some of the newer biomes are frustratingly rare or commonly distant from spawn.

As was mentioned in the comments, to more easily verify the convenient placement of a given biome in a given seed is to test it in AMIDST. That way you won't have to fly around in creative mode to tell what the biome layout will be.