I'm interested in finding different techniques that can be used to create vanity addresses with a BIP32 address.
For example, can any of this computation be offloaded to a dedicated server, or a 3rd party?
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You can do this but the advantage of HD wallets effectively diminishes. You can simply brute force by iterating over all the indices of the HD wallet until you find one that has the vanity characteristics you want. However, its possible that it is sufficiently hard enough to find that you will have to save off the private key anyway.
The entire point of HD wallets is that you only need the master private key/seed to generate all your addresses. If you end up with an index that so far out from the last used address, you might not be able to find it in the future without also having saved the private key for the vanity address.