Maybe I should've bid 3
♣ over 1N, but I'm convinced an immediate 2
♣ (natural) would've been wrong. It doesn't take up bidding space, and partner doesn't know to preemptively auto-raise with club support. The only advantage to an immediate 3
♣ is that I might (but might not) avoid an auto-double (but partner might unfortunately take me for a near opening hand). Also, at that point, I don't know that partner has around half the missing high cards.
I'm a little leery of opening 3
♣ with a decent 4 card major. After all, the weak field can work for us if we have the cards and we're the only ones declaring the right contract.
(I'm playing with someone who would've been a good bidder in 1965. It's a challenge adapting to his system (which is about halfway between Goren and SAYC), not so much in knowing what bids mean as in psychologically accepting sitting for average-minus on a lot more hands than I usually have to. We're in a small remote town, hence no real choices for either of us.)
Some of your strategies for randomizing are overestimating the field. You're thinking that the other pairs will play 2N and not handle the bad split as well. Given the field, it's quite possible the other contracts are 1N, 3N, 2H, and 3S (all by E/W), and in that case, we likely have a 12.5% before the first trick at either 2N or 2NX, no matter what our lead is.
But really, the title of the thread is quite accurate. I didn't exactly bid 3
♣ seriously, since one can't exactly take such a club game too seriously, and we've agreed that I'm allowed a couple stupid competitive bids a session out of my frustration at his system. I'm just wondering roughly where between 10% and 60% such an action is.