I remember having read that the VampireScript could be edited so that you could become a vampire again, even after having been cured (I have the Vile Lair, so curing myself isn't exactly a problem), but now I can't seem to find the topic where I saw this particular bit of text. Does anyone else know what can be changed in the script so that the player can become a vampire whenever he/she wants?

Most vampirism overhauls allow for that, 'vampirism' in vanilla is nothing more than a bunch of script instructions in the VampireScript that add spells and keep track of time for the stages to advance.
So if I remember correctly: When you get cured, the global PCVampire gets set to -1, preventing the VampireScript from doing anything meaningful, so you have to set it to 0. The quest variable vampire.hasdisease, which tracks if you have porphyric whatever, gets set to -1 upon transformation into a vampire, and the quest variable Vampire.daycount, which tracks the number of days you've been carrying the disease, remains at 3 once you transform into a vampire (if you set the other two to 0 but forget daycount, you'll transform immediately after sleeping), so you also have to set them both to 0 after the player gets cured.
Use at least the VampireScript fixed in the Unofficial Oblivion Patch as a guide, as it fixes awful bugs in the vanilla implementation. Or you could just change the VampireScript to your likings for a twist in vampirism's implementation, including possibility of becoming a vampire several times, like I did in my vampirism mod.