I have terrible luck with tires?

Not really that hard to find 15 in tires around my area or online. Have you looked at Tire Rack or A place like Mavis or even Wal Mart? I just looked and walmart shows a couple of good tires for the Blazer The Goodyear Wrangler Trail Runner if you want a more aggressive tire or the Uniroyal Laredo HT for a more street design, I've run both on mine with good results. The Wranglers are a bit noisier though. You can order both online and have them shipped to your local store for install.

However if you wanted to go to a 16 inch tire you would need 4 new 16 inch rims to fit and for a tire that is the same size so it doesn't rub you would use a 235-70/16

235/75 are about the most common 15 tire still out there and because that is a 4X4 you need to run the same tire on all 4 corners if you don't want strange handling in 4WD. The Blazer is pretty heavy and needs a decent tire to support it. Unfortunately tire prices have gone way up in recent years and with modern cars running 16 up to 20 inch the old common sizes are just not that popular, even though there are still tens of thousands of vehicles running them.
As you are a delivery driver I would spend the money on 4 new tires, it will make it much safer to drive and they will last a few years. This is especially true if you drive in rain or snow, a good set of tires might mean the difference between delivery and a wreck.
As for what tires fit in place of the 235/75, there really are none that are available anymore.
To keep the tire diameter in range for the driveline and the ABS as well as the speedometer you would need to alter both numbers to stay around the 29 inch diameter. and because the tires are already running close width wise you really don't have many choices without doing other work. They came from the factory with 235/70-15 and 235/75-15 tires
If you want to see other sizes you can look at this tool
https://tiresize.com/comparison/
You enter in the OE tire on 1 and then click "show alternate sizes" It then gives you a list of tires that match diameter, BUT you need ones that also fit width, for that you will only se a couple choices. The narrow one is 225/75-15 which is more a trailer tire or dually tire.
Just one of the things involved with owning an older vehicle. At least it isn't one of the popular RV sizes like the 16.5 tires run on 50% of the van based RVs out there. There are 2 companies that still make those and they only do a limited run every couple years.