Do I traverse by saying, since the same claim set applies to all three species, that there is no undue burden on the Examiner to search all three?
I have only found a requirement for serious burden if there is a restriction between inventions, and not mere species, although the MPEP is clear that distinct species can also be distinct inventions (without providing any guidance as to when this does, or does not, happen, other than defining generic claims). The closest the MPEP comes, perhaps, is the discussion of distinct, non-independent species in 808.01(a): "Where there is a relationship disclosed between species, such disclosed relation must be discussed and reasons advanced leading to the conclusion that the disclosed relation does not prevent restriction, in order to establish the propriety of restriction
Since I'm still required to make an election, do I just arbitrarily pick one (say circular)?
Yes, I would pick an arbitrary one, and assert that all of the claims read on all of the species (if they do).
What's the consequence of the election on claim scope, since the claim has no limitation with respect to shape?
There should be no consequence. Although restriction requirements limit applications to particular inventions or species, I have never heard of defendants successfully relying on the applicant's election to limit claim scope beyond what it would otherwise be.
On the first office action on the merits, will I be required to amend the claim to "a circular tabletop"?
This is a good question. MPEP Chap. 800 does not appear to explicitly
forbid the examiner from requiring such an amendment. However, statements like the following:
"Upon the allowance of a generic claim, applicant will be entitled to consideration of claims to additional species which depend from or otherwise require all the limitations of an allowable generic claim as provided by 37 CFR 1.141." ¶ 8.02 Election of Species; No Species Claim Present
Clearly indicate that, although the applicant must elect a species, a generic claim reading on the species will still be examined. However, narrower claims drawn to non-elected species will not be examined.
Restriction requirements based on claims makes sense, but election of species based on figures has me confused.
The figures are just a crutch. They are used to sort of out mutually-exclusive embodiments that are non-obvious relative to each other.