We also used the string method before we got the LTU. I bought the LTU after I did the string method and was a little off, my eyes are getting old. Now with the LTU we are always dead on and can tilt it as we go to make sure the pipe is still going straight.
Deeretime we have used a regular slope laser when our pipe laser died one time, lucky we had a laser with slope mode and didn't have to stop the job that day. You could do it with a non slope laser but would have to figure out the rod for each end of pipe. And a laser in slope mode setting pipe wouldn't be of much use for checking other grades because if the slope. But a pipe laser is definitely easier and faster.
And to the OP, I don't know what could be faster than the string method with the LTU coming in close behind it. It doesn't take me that long to set the LTU up and then I leave it for the day just to check and verify, and I don't know what could be more accurate.
Day, that half day we used our slope laser the line did come out perfect, but it was not easy. We had to use the rotary slope laser and the LTU, the rotary to keep the slope of pipe right and the LTU to keep the pipe straight. And then you have to have a couple of extra guys helping, one to help bar the pipe up and hold the rod and the other to look through the LTU. Deeretime like I said it is definitely easier with a pipe laser, for most of our jobs with pipe in the 12" range I just have one guy in the ditch gasketing the pipe, then setting the target and lining up the pipe to the laser