I suggest, that while searching for your "Holy Grail" bike, that you buy a used (but in decent shape) late 80's or early 90's, steel, rigid fork MTB. I see them in CL for <$100 all the time. Look for Treks and Specialized brands. I find these bikes a real bargain and almost bomb proof.

When you finally find your "Holy Grail", then this bike will make a great "Oh, ****!"/back-up/bad weather bike.
' never hurts to have a reliable back-up bike, IMO.

Good luck and have fun hunting your bike!

Edit: Nevermind. I didn't read the part that you already have a an old MTB.

This is what I did, except that I bought the first steel bike new instead of used :-(. But after a couple of months of riding, I realized that my particular commute demanded internal gearing (lots of stop-and-start at intersections) and internal brakes (lots of rain). So I picked up a Trek Soho, which really suits my needs perfectly (and not having a chain to deal with is a big bonus).

I was tempted early on to drop several hundred dollars on a better bike the first time around, but doing so before having done my commute several times I would have ended up with rim brakes, a derailleur, and an unnecessary suspension fork. I'm sooooo glad I waited. That said, my commute is 13-15 miles with hills; if yours is 5 miles flat then I would probably worry less and most any bike will suit you fine.

Chainguard really limits your selection. I am very impressed with this add-on from Velo-Orange. It opens up the possibilities to some more models that don't come stock with chainguards. https://www.velo-orange.com/voalpoch.html

OP: I've been pretty impressed with the value I've seen in the Schwinn line. I'm confused by which locale you're looking for your LBS in, since you are moving. But a LBS you're happy with is good. You may also want to look at the REI Fusion and Transfer, higher than your budget, but gives you an idea of some of the boundaries and you may find with rebates, coupons, etc. from time to time.