Taking an academic pseudonym?

Complementary to your own suggestions and the ones in the other answers, you could consider creating an ORCID (or of course any other unique researcher/author ID) and using it in all publications. The benefits here:

• By adding a unique identifier to your name, the name collisions can be resolved.
• If your change your name at a certain point (e.g., if you decide to change your name as you suggested in the question), the ID will remain the same. Therefore, you even might be able to postpone the decision whether to change your name.
• Since you mention online identity and SEO: At least ORCID comes with a profile web site (I am not familiar with other ID systems), where you can add your personal information and even maintain a list of your publications. Usually, a link to this profile is added to the publication, so readers can follow it. As to search engine optimization, I am not expert here but I would guess that the outcome of those algorithms improves if there is a unique ID that groups your contributions together.

Of course, all those ID systems are quite recent and might not be accepted (yet) by the journals and/or researchers in your field. Nevertheless, I would give it a try since it comes at no cost (which I presume won't be the case for changing legal documents).

If you have a middle name, then you could add a hyphen to derive a new name, e.g., Alpha Bravo Charlie could become Alpha Bravo-Charlie.

Does this seem like a worthwhile idea?

Yes

Could there be any issues with having different legal and professional names in a university IT system?

Yes, but this will vary university to university. An obvious problem might be the assignment of email addresses, e.g., [email protected], but this can be resolved by a polite email.

Should I change my undergrad enrolment to be under my new academic name?

This mightn't be possible, you'd need to justify (perhaps legally) a reason (which you cannot legally prove).

How about when applying to postgrad/PhD programs?

You need to be careful: Don't commit fraud. Being employed under a non-legal name is possibly illegal, publishing under a non-legal name is not.

could/should I get degrees reprinted (once I have an established career) under my academic name, rather than my personal name?

Some institutes may question a certificate in the "wrong" name, others won't, many won't check.

Are there any hairy issues that could arise from this, which I might not have considered?

You might inadvertently commit fraud...

EDIT: I had assumed a full name clash (that's what the OP wrote). If there's merely a partial name clash, e.g., Alpha Charlie, and the OP has a middle name, then I suggest that the OP simply uses their full name, e.g., Alpha Bravo Charlie, as their name, that is, they always use their full name and they don't drop their middle name.

EDIT II: The comments suggest using an initial, e.g., Alpha B Charlie or Alpha B. Charlie, but I'm not sure whether this helps for SEO; a full name, e.g., Alpha Bravo Charlie, seems more likely to succeed in terms of SEO.

A former colleague has effectively swapped their middle and family names for publishing purposes (I believe their given middle name is also in some way inherited). The now surname is (for native English-speakers) simpler and more natural to spell and pronounce than the legal one, and they use the initial of the legal surname as a middle initial. The new name is simultaneously academically unique and intuitive for people from many cultures (working in English).

Applying this to Dorothy Hodgkin as an example would give Dorothy H.Crowfoot.

This is a slightly bigger change than the one you propose, and so far seems to work well.