Along the way, I came across a technique to disable LTE and leave HSPA enabled.
LTE is a notorious consumer of battery and HSPA typically yields around 10Mbps down so even without the "No Service" issue turning off LTE is probably worth considering.
First go to the Dialer. Enter *#*#4636#*#*.
As soon as you enter the final asterisk, your phone should display a "Testing" menu.
Tap on "Phone Info".
The 4G LTE Switch app in the Play Store will take you directly to this menu. Scroll down until you see "Set preferred network type:"
Just below that you'll see the current network type, probably "LTE/GSM auto (PRL)" and a little "twistie" over to the right. Remember what that value is so you can reset to that if needed.
Tap on that "twistie."
Scroll through the resulting menu.
Tap on "GSM auto (PRL)". Now tap on the back button until you exit this menu. Don't just tap the home button.
Here's the download speed I'm getting.
You may have to repeat this after you restart your phone.