Similar to @Courtney King's advice, I used to prepare "appraisal packets" on all my SFH refi's. It would include a cost breakdown of the improvements made, before/after photos, along with the appraisal at purchase (which may or may not be a good idea...but I felt more good than bad). The packet was very professional...color, TOC, tabs, and bound. I also met the appraisers at each of my properties to make sure if was "professionally presented". I certainly didn't get in anyone's way or try to push for a high value. But these little things can make a difference.
I also don't want to down play the $3-5k. But like @Kenneth Garrett said, you will delay the process, likely pay for another appraisal, and might still not get what you want. There is definitely subjectivity built in.
If it makes you feel any better...we did a refinance on one of my multifamily properties and it was "let's just say 6 figures" below where it should have been. My appraiser was a trainee. It was his first appraisal. Some of the techniques he used were unthinkable. My lender challenged it all the way up the chain. They didn't budge. And unfortunately, I did not have time to order another appraisal (not to mention that these are much more expensive than a standard SFH appraisal). Licked my wounds and moved on. Maybe I'll catch the right break when it's time to sell or if I refi again.