I would be cautious with this type of speed building. I'm not a professional nor a banjo player, I play guitar & a little mandolin but I would have to think that building speed is about the same process in anything & I don't mean just music.
Take a pitcher for example: A guy may be able to throw 90 mph, but if his technique is poor & his form isn't consistent, he won't be able to throw strikes. He has to start slowly developing his technique until his form & movements are as perfected as possible. Then once it becomes natural & muscle memory has developed, he'll be able to throw the ball harder & control those 90 mph pitches & place them right where he wants them. This also develops confidence which is another key in doing anything good & with precision.
My experiences with trying to play too fast too soon usually result in terrible technique, sloppy playing, poor tone & (this is the worst of all), PRACTICING MISTAKES & then ....... discouragement in learning the song altogether.
Most professionals will say to work on something at only the speed fast enough to where you can play it cleanly with good technique while maintaining good tone. Once that's accomplished, move up to a faster tempo & again & again. It may take awhile to reach your desired speed, but being able to play through it cleanly with good tone is most important.
Speed excercises are good tools as well as playing other songs. They will all lead to playing that one song better & faster. You'll sound more professional playing a slower song cleanly with good tone, timing & precision, than trying to play fast, missing notes & just sounding plain bad.
Everything I've said is simply my opinion. I may be wrong. What works for you may not work for others & what works for me may not work for you. There are no rules & we're all in this together trying to be better musicians. So find what works best for you. I might just try that double speed step-up practice thing myself & find out it works great. Just be very cautious of practicing mistakes with bad technique. Hope this helps...........