Can I run 275ft underground cable to pole barn?
Your first, and only question that I see, is whether or not you can run 275 ft. of underground feeder wire to your barn.  The answer is: Yes, you can provided you use wire large enough so that the voltage drop at the barn is acceptable to your use.  As noted in your question, the commonly accepted value is 3%.
For long runs (i.e. large wire sizes) Al wire is significantly cheaper than Cu and the only benefit from using Cu is that you will use a smaller wire size.  The overall performance of a properly size Al wire vs. a properly size Cu wire is the same.
I do question your 100A load figure here.  Are you going to be running multiple tools at one time?  You've mentioned only a welder and a compressor but those together will take only 40A.  I can't imagine that you'll be using anywhere near 60A for your lighting.
BTW - you might consider LED lighting instead of fluorescent.  The cost difference is not that great any longer and LED use quite a bit less power.
I don't get your 1 AWG figure, however. Using the Southwire calculator at:
Southwire Wire Calculator
returns a recommendation of 4/0 :