How to handle solo 401k contribution limits across two self-employment entities?

Differently stated, does the 'disregarded entity' treatment of the one-member LLC also apply for the 401k contribution limits?

Your question is a bit confusing. If the LLC is disregarded for tax purposes, then it is disregarded for all tax purposes, you can't pick and choose. So yes, if the LLC is treated as a sole proprietorship for tax purposes, then the 401k contribution limits are based on the rules for solo 401k plans.

The net income and self-employment tax must be computed for each business form, and then two 401ks are needed, each with their own limits?

No, the net income and self employment taxes will be computed once per person, no matter how many schedules C they end up with.So are the retirement contributions, on schedule 1. Your second link covers that.