Well, the reasons for transits are obvious enough; planets passing in front of the Sun. So the key question would end up being why only Mercury and Venus pass in front of the Sun.
Under the typical model, this is obvious enough. You can place other planets to in fact be higher than the Sun, so while they might occasionally vanish behind it, they'll never be in front. The issue then, here, is the size of Mercury and Venus, as you brought up.
In that case, personally I'd take issue with the measurement you used for distance to the Sun. Yes, that figure has been used a few times over the forum, but the methodology behind it was flawed; it used Eratothenes' experiment assuming a flat Earth to calculate how far away the Sun was, which is problematic because trying the same experiment at a different time of day would give an entirely new distance to the Sun. So whatever's going on with the Sun under FET, it can't be that intuitive. As such, that figure would be unreliable.
DET's where it gets trickier, because while it has an answer to the planets, my understanding of the model is that all the planets ought to be able to pass in front of the Sun. The size and distance to the Sun are much trickier under that model, so on that part of your argument fails as it could easily be more than 32 miles across, but I can't immediately say why only Mercury and Venus pass in front of the Sun. I'll see if JRowe's said any more about it when the search function starts working again.