The new rules that went into effect on 5/1 are called HVCC (home valuation code of conduct) - search the boards here and you can find a few posts from an appraiser who gives his thoughts.
Unfortunately appraised value matters more today then at another other time - I have posted here a few times about the importance of getting an appraiser to give you values - meaning you can't rely on your own comps - on Realtor comps anymore - you really need to spend the $$ for a value check / desktop or actual appraisal…can save a lot of headache before you buy a property.
Unfortunately there isn't' a lot that we can do about it. I did hear a rumor that someone (I think a congressmen from Alabama or Mississippi) has offered up a bill to stop HVCC for 18 months - about all we can do is contact our federal reps and tell them to support or offer up their own elimination of HVCC.
As you found out - going to another appraiser didn't help - so unfortunately there isn't much you can do.
Also - not sure HVCC is to blame in this case - would need to see the appraisal and other comps out there but things like time adjustments are gone so the appraisers have no choice but to use whatever has sold in the last 3 months - that also means your value could change tomorrow + or -. If there are only three comps and they at $280K - if another comp comes in at $400K tomorrow then your value goes up a lot - if another one comes in at $200K you just lost a lot - so in a market where there are few sales the next sale really sets the market.
So all you can do is wait on your refi - or if it still works as you said you can go through with it - just be 100% sure you pay for the value check or desktop or full appraisal on the investment (if your financing for sure!) to be 100% you can get the deal done or be prepared to kick in more $$ or pay all cash.
Just know with financing the lender can no longer communicate or select the appraiser - so even if you get something done upfront there is no guarantee that the final appraisal that is used will be at the same value - just have to have plan B (generally more $$ to put in the deal) to make it happen.