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I really don't want to use rectangular bases in my (40K) daemon army, so I'm trying decided what I should base my chariot conversions on.

The most likely options seem to be:

a round 60mm (i.e., dreadnought size) base (rather small, compared to the WHFB chariot base)

a Trygon base (quite big -- bigger in surface area than 2 dreadnought bases lined up next to each other -- almost too big to be playable)

a converted option, using a 60mm base sawed in half, stretched/elongated to oval form.

The issues would be appearance and (more important) fairness: as these creatures will be deepstriking in, they need to be big enough to create a fair mishap hazard.

What would be fair? Which option will be most acceptable, both for friendly games and in tournaments?

Here's a pic, lining up a pair of 60mm bases and the trygon base:

For what it's worth, I would be fine with both options.

Here's a fourth option that i suggest you add to your poll. 'Lozenge Style WFB Chariot Base'.
I'd use a chariot base from wfb and give it the lozenge treatment with 60mm base ends.
Seems the most fair to me.
If you don't want any straight edge at all i'd go for the stretched 60mm bases.
Trygon seems way too large and the 60mm is just plain cheating!