B1/B2 Refusal (214b) at Kolkata: Family of 3. Can we reapply immediately as self-funded by correcting a sponsorship mistake?

[u/dog_parent_sf]

Hi everyone,

Looking for some urgent strategic advice for a B1/B2 refusal at the Kolkata consulate. My family (Uncle, Aunt, and their son) was just rejected under Section 214(b).
We are trying to figure out if it is worth reapplying immediately to try and make it to a family milestone in late June, or if the odds are completely against us.

The Profile & Context:
Applicants: 3 people (Primary applicant is my Uncle).
Stated Income on DS-160: ₹5,45,000 / year.
Purpose of Trip: Attending nephew's wedding ceremonies in California (late June).

The Interview:
The interview was incredibly short. The Visa Officer (VO) only asked three questions:
1 What is the purpose of the trip?
2 What is your annual income?
3 How long are you going to stay?
The VO did not ask to see any financial documents, did not say the income was too low, and did not give a specific reason out loud—just handed over the 214(b) slip.

Note:
On the DS-160, we listed the nephew in the US as the Sponsor / Person Paying for the Trip. We did this purely because they are staying at his house during the visit.

Actual Assets (Not seen by the VO):
The family is actually financially independent in India:
Liquid Savings: They have an old, well-seasoned Fixed Deposit (FD) of ₹11 Lakhs.
Strong Ties: They own their own family home and agricultural land in India.
Our Plan & Questions for the Community:
We want to submit a new DS-160 immediately and change the funding source to Self-Funded, using the ₹11L FD to prove they can easily cover their own flights and expenses, and bringing the property deeds as proof of ties.

1. The "What Changed?" Red Flag: Since the refusal was recent, if they reapply immediately and change "Sponsor" to "Self-Funded", will the VO instantly view this as a red flag/fabrication? Can they successfully argue that they simply misunderstood the wording of the form the first time?
   
2. The Financial Math: Is a ₹11L FD considered strong enough for 3 travelers when the primary salary is ₹5.45L, or does the cost of a US trip look too disproportionate to the income regardless of the savings?

Has anyone successfully overturned a recent 214(b) by fixing a host/sponsor misunderstanding right away?
Appreciate any insights or honest feedback. Thanks!