Since shares are constantly dropping off the chain, you have to keep finding shares, otherwise as your shares drop off the chain, your payout will also drop?
If you have a dry spell your payout will drop, because more shares are dropping off than are being found.
Likewise if you have a hot spell your payout will increase as more shares are added than dropped.
How do dead and orphaned shares fit into this?
Is this a reasonable accurate understanding?

Yes, this is largely correct. Dead/orphan shares can still be valid Bitcoin blocks that pay the pool. The Dead/orphan refers to the share-chain, not the Bitcoin block-chain.