"Hello! Is it possible to replace my current sink with a single basin sink without taking off the granite counter top?"
Yes. I've done it a hundred times and haven't ever pulled a top to do so.
"My sink an undermount that I assume is glued to the bottom of the granite?"
It may be "glued", but is more likely siliconed. Simply release any mechanical fasteners, disconnect the plumbing, then drive a stiff scraper between the bottom of the stone and the sink flange. That thing's coming out, believe me.
"Granite sink opening measures 28.5" by 15.5"."
I suggest the 3118 from MRDirect. You'll have about a 1/2" negative reveal (the top will overhang the sink) and the corner radii may not match perfectly. I've used this sink many times in this application. Your sink will come out of and the new sink will dunk into your existing cutout.
"If this IS possible, what type of contractor person do I contact? Or should we try to DIY it?"
Some plumbers will take this on. You don't say your level of DIY skill. If you're moderately skilled and experienced, you shouldn't have much trouble. My last one took me two hours complete. Use the pipe-clamp-through-the-drain-and-2x4 method shown here, please.
You'll also want to install the sink with (2) Sink Straps from Regent Stone Products. No clips, please. Side to side, behind and in front of the drain.
Same sinks, nearly the same cutout, before and after:
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