It complicates it if the payout currency and traded currency change - eg a quanto.

Are you sure that the minimum variance approach the multi-variate regression approach aren't doing the same thing?

I would take a step back and ask the usefulness of such a calculation. Are you calculating dividend yields from vanilla option prices? In practice I have found this to be a first-order approximation. Also in most instances you calculate the dividend from $(r-\delta)$ (requiring you to have some opinion as to the structure of $r$) which is increasingly difficult in the durations you mention.

Can you elaborate? If 1 call option is 0.5 delta, then two call options are 1.0 delta and you would need 1.0 of the underlying to hedge it (although this hedge ratio will, as usual, change)

You've changed the problem so the results will surely change. The criterion you're describing is just for long-term growth. There are many variations like "How to Gamble if you Must" (subfair games), "How to Gamble if You're in a Hurry" (finite horizon), etc.

I agree that brokers not allowing shorts provides a price bias. I don't agree with the robustness of the marketplace and the ease of access to influence the price higher (it provides those same benefits to short sellers).

I'm familiar with the replication formula... so is the distinction very clearly "path dependent payoffs cannot be replicated" with vanillas? Are there replication methods (separate from Carr-Madan) for path-dependent payoffs?

Professor Nielsen of Columbia wrote what I would consider the canonical resource for intuition behind this in a BS world.