A better method of bending just the loop is to grab a pencil, and use the pointy end as a mandrel. You'll have a choice of diameters, and you can bend the loop easily by holding down the very end of the loop with your fingernail, and bending just the loop section.
Your loop should look something like this:
For any loop end string, this method gives you a hooked loop that will seat easily on those weird tailpieces. Mandolin players are not singled out for punishment; lots of banjo players have to deal with bending strings to fit tailpieces, too.
Don't forget that there is no real difference between ball-end strings (as on guitars) and the loop end strings. With some practice you can cut the brass ball out of a string to make it a loop end string. The loop is smaller, but usually works fine. So you can use appropriate gauge ball end strings in a pinch.
Don MacRostie, builder of the famous Red Diamond mandolins, reminded me to mention that the twisted loop end usually has a little sharpie sticking out at the end of the twist:
So don't forget to orient that little sharp point downward if the string goes over the top of your tailpiece, like this:
That way it won't catch on your arm or sleeve.
The tailpiece isn't the only nasty piece of business in restringing mandolins.
All mandolins have tailpieces and moveable bridges. That means that the bridge will fall off if you take all the strings off at once. Some people say that it is not healthy for an instrument to have all the strings taken off because the instrument is built for high tension and will suffer if the tension is released.
These people are wrong! All stringed instruments would be likely to last longer if they never had any strings on them. It's a good idea to release the tension if an instrument is going to be stored, shipped or exposed to high temperature.
It's not a bad idea to take off all the strings if you're going to clean up the instrument. We always restring instruments in the shop by taking off all the strings and at least wiping the dust off underneath.
Personally, I change my own mandolin strings a few at a time because I hate readjusting bridge position. At least once a year, though I like to clean things up a bit, so I take them all off to make the cleanup easier.
When the strings come off, the bridge does too, but it leaves some sign of where it was, so you can use that as a starting point for relocating it. This new Phoenix bluegrass mandolin has a little pressure mark you can see with the reflected light from my overhead fluorescents:
It's easy to spot which way to orient the bridge on the top. Just notice the size of the notches: big ones for bass strings, little ones for treble:
When replacing the strings on a mandolin, I like to install the first string with the bridge off, leaving it a low tension. Then I can lift the string up, and stick the bridge under it, right on the impression in the top.:
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