Changing Lender after Appraisal

[Eka Linwood]

So, this is probably my fault for not doing a better due diligence ahead of time.

We got under contract early Jan for a closing date of Feb 20, and this is my first time buying a house. I got a pre-approval from Lender A, and right after the Seller accepted the offer, I went shopping for Financing.  I went to Lender B, C and D.  Only Lender B were able to get back to us with a loan estimate.  Lender C and D were not able to, due to the various complexities on the deal.

Just last week, I got curious and read up on FHA rates some more. I found a new Lender (Lender X) that is publicizing 0.25% better rate. Now, my credit score is excellent and DTI is very low, so I should have no problem qualifying for the best FHA rate. I do prefer to sign up for the least amount of down-payment (FHA 3.5%) though, so there is that.

Since I thought this issue is closed, I ended up getting this Lender to proceed with the whole process.  The only thing pending right now is the appraisal (ETA: Jan 31) and the Home Insurance (After Appraisal).

If Lender X rates (2.75%) come in significantly below Lender A's rates (3.0%), I see two scenarios:

• I move to Lender X - potentially jeopardizing the deal and have the Appraisal moved to Lender X or maybe paying for another appraisal altogether.
• I stick with Lender A and ask them to match this new Loan Estimate from Lender X.

My questions are:

• Would it be ethical to do this to the Lenders? 
• Is it possible to "move" appraisals to the new Lender?
• What are the chances of this action jeopardizing the deal?