Question: I seem to be hearing many different vocalizations of the name, and I'm not sure which one is correct. The last thing I want to do is "erroneously" drop the name in a meeting, and someone feel the need to correct me. So is it pronounced "Ess-Cue-El-ight", or "Ess-Cue-El-Eye", or something else entirely? Is there a citation from one of the project developers lurking around the internet that explicitly states the correct pronunciation? Would really appreciate some clarification!

Two video sources:

<https://youtu.be/Jib2AmRb_rk>

<https://youtu.be/giAMt8Tj-84>

Edit:

Kind of embarrasing, but I didnt even realize that the first video link was actually the creator of SQLite, Dr Richard Hipp, and he pronounces it as "Ess-Cue-El-Ight/Eye". So that pretty much confirms the correct pronunciation is somewhere in that modicum of a ballpark.

Answer: 
There are in general two ways to pronounce 'SQL' by itself and that leads to two reasonable ways to pronounce 'SQLite'.

'SQL' is pronounced either as 'ess queue ell' or 'sequel' (in IPA /'es 'kju: 'el/ or /'si: kwəl/ respectively).

This leads to 'SQLite' as either **'ess queue ell light' or 'see quell light'**, which in normal pronunciation comes out as 'ess queue ehlight' or 'seek quellight' (or in IPA /'es 'kju: 'el 'lait/ or /'si: kwə 'lait/ respectively note the syllable accents)).

The two varieties for SQLite are probably in the same variation as SQL.

Note that the inventor pronounces it the first way but in his accent (Estuary English) makes a glottal stop out of the final 't' (or even drops it altogether). In GenAmE the final 't' is unreleased and so may also be hard to hear for non-native speakers.
SQL by itself [is (or can be) pronounced](https://english.stackexchange.com/questions/7231/how-is-sql-pronounced) as "sequel".

Therefore it seems logical that SQLite is pronounces "sequelite".

Edit: According to your edit the creator of SQLite pronounces it as "Ess-Cue-El-Eye". I don't think that's how he actually pronounces it, he's just talking fast and sloppy. He pronounces it (in my ears at least) as "Ess-Cue-El-ite". And later in that presentation he explicitly says that he doesn't care how you pronounce it.