An obvious solution that handles steps 1–5 (changing the secret) would be for Alice to generate a random encryption key $K$ (of, say, 128 bits), encrypt $S$ with $K$ to generate $P$, and then share $K$ with the other participants using a conventional secret sharing scheme such as Shamir's.
Indeed, if all the shareholders (other than Alice) are always needed to reconstruct the secret, you don't even need to use Shamir's scheme: trivial XOR secret sharing (where Alice gives all but one of the shareholders a random bitstring, and gives the last one the XOR of all the other shares plus the secret) will do the job just as well.
Indeed, with XOR secret sharing, steps 6 and 7 (adding and removing participants) can also be achieved: Alice simply sends random bitstrings to the new participants, computes a new key $K$ by XORing together the shares of all the active participants, and encrypts the secret $S$ with the new $K$ to obtain the new $P$.
In fact, if the key $K$ is (at least) as long as the secret $S$, you don't even really need a separate encryption step: as long as $K$ is random, you can simply XOR $K$ with $S$ to obtain $P$, making this an instance of one-time pad encryption.
This also works with Shamir's scheme, as long the reconstruction threshold equals the number of shareholders; Alice can just send random shares to all the shareholders, reconstruct a (random) key $K$ by applying Shamir's reconstruction algorithm to the shares of the active participants, and use that key to encrypt the secret.
However, note that all these protocols suffer from some fundamentally unavoidable flaws:
if the shareholders can remember old $P$ values, they will be able to reconstruct old secrets even after Alice has changed them, and
if removed shareholders can remember their old shares (and the old $P$), they can still reconstruct the secret (assuming the other old shareholders cooperate) as it was before they were removed. However, if the secret $S$ is changed whenever participants are removed, the remove participants won't be able to contribute anything useful to reconstructing the new secret.
Edit: Based on the comment below, it seems I misunderstood the question: you want each of Bob, Charlie and Dave alone to be able to reconstruct the secret using $P$.
A simple way to achieve this would be for Alice to distribute different random keys $K_i$ to each of the other participants $i$, encrypt her own key $K$ with each of $K_i$, and combine the ciphertexts into $P$.
Of course, the down side to this method is that the length of $P$ would be proportional to the number of participants, which could be a problem if that number is large. However, I'm not sure if it's possible to do any better, and I suspect it may not be.