Perhaps this Chicago Faucet, which has a 12" reach and is only 8 1/8" tall? You can add a swivel aerator to it, or consider some of their 13"–26" double-jointed swing spout faucets.

Thanks for the comments thus far! Unfortunately, the large coiled looking faucets are a bit tall and obtrusive for her liking.

The current faucet works, but has a pretty bad leak around the main shaft. We're looked at replacement parts, but do have some concerns if we take it apart and it's broken beyond repair, that we will be in an even bigger pickle. We may still have to go that route!

The suggested Chicago Faucet almost fits the bill, minus the single handle for turning the water on and adjusting temperatures, which, for her is a bit of a big deal.

Thanks again for the comments!

Sometimes you need to just move on I love a single handle maybe if she had one she would learn to love it too. The one she has looks old so maybe a newer better one is on the horizon .

Any number of the single lever arc (non coil!) pull down faucets should do the trick. They have sprayers that pull down from the spout, and can cover the entirety of a sink. Most have buttons on the side of the faucet head, that provide a variety of sprays. I use the gentle berry spray on my Koehler Artifacts faucet, the most.

I‘m quite familiar with the type of faucet/aerator combination your mother has. Back in the 70s and 80s, I had that, too. Believe me, these modern pull down faucets are a vast improvement.

Here’s my sink and faucet. The Koehler Artifacts comes in two pull down sizes. I have the taller version. Click to enlarge.

Google Koehler, Delta, Moen, Grohe...or just “pull down faucets”. Browse the sites, and see what appeals. When your state reopens from Covid-19 lockdown, perhaps go see the faucets in stores.

@kdvetter If she requires a single handle and side-sprayer and nothing else will do, I'm pretty sure Chicago would build this fixture with that 12" spout on it. They used to have a pretty robust configurator for Frankensteining faucets, but if it's still around I can't find it online.

Thanks again for all the comments! I thought I would post just one more photo of the entire sink to give everyone a sense of scale here. It's a pretty wide setup - 38" width from the inside of the far left basin to the inside of the far right. The current faucet reaches about 5" inches into each of the side basins (hence our concern for having the longer spout reach. The comments so far have given us a couple options by the sounds of it!

!

12" reach but 6" high:

• Moen M-DURA Commercial Kitchen Faucet Model: 8711

10" reach with pull-out sprayer:

• Houzer Calia Pull-Out Kitchen Faucet with CeraDox Lifetime Technology Model: CALPO-561-PC
• Elkay Explore 1.75 GPM Single Hole Pull Out Kitchen Faucet Model: LKEC1041PN

This site have options to see the different heights and spout reaches. I was also looking for reach more than 10 Inches

Single Handle Faucets at Build.com

ALFI brand AB2038-PSS Pullout Spray Kitchen Faucet | Build.com