What can we believe about Yetziat Mitzraim?

Putting aside the creation story, the most historically difficult event in Tanach is The Exodus. The historicity of The Exodus has been debated into the ground, and I don't intend to go into anything but a cursory explanation of my beliefs (and only if necessary), but yesterday I became curious as to what - from a traditional point of view - we are permitted to believe about Yetziat Mitzraim.

So I did what any reasonable person would do, which is ask Daniel, an intelligent and frum student in my existential philosophy class. (Daniel also happens to teach in a yeshiva).

Simply put, the biggest problem with the Exodus - ignoring the miracles - is the number of people involved. Whether directly or indirectly, the claim of 2+ million Jews leaving Egypt en masse, hanging out in the desert for 40 years, and then settling Canaan is not historically possible.

Many Bible scholars have commented on the word eleph, commonly translated as "thousand," arguing that the word really means something like "troop," "family unit," or "clan." Other scholars have pointed to a historical trend toward (very) systematic number inflation.

So my question to David yesterday was whether a traditional perspective allows for the belief that yetziat mitzraim occurred, but the word eleph has been consistently misinterpreted and only ~20,000 Jews left Egypt.

I'm not sure if Daniel really thought through what reinterpreting eleph would do to countless maamarei chazal (or whether he was just giving me a kiruvy response), but he said that as long as the "motivation" behind the reinterpretation is good, there is no problem. In a followup question Daniel confirmed that reconciling the Biblical narrative with "scientific" history was a fine motivation.

What kefira! Or is it?

Thoughts?