RE: Sink tip or sinking fly line?
For smaller streams with bigger runs where I don't have to fish the whole run I like loop on sink tips. If it is bigger water where I'm fishing 30'+ of line I'll go to integrated sink tips. I did what you're thinking and cut up some old sinking lines. It works, but isn't the best solution unless you want to go through weighing them all out for a particular rod or a few rods. I also made some full lead core heads from lead core line (mostly for big flies in the surf). Can be fun to cast when you really zing one (a 50' head on my SCIV 10 wt will go 140' and still turn over a 9' leader and clouser).
Anymore, I carry a couple of the lead core loop to loop leaders from gudebrod (I think). I fish a standard WF floating line for everything and my multi purpose lines all have a 6" 25# mono butt with a perfection loop on them. If I get into a run that is deep and fairly long I'll throw on one or two of them, then loop on a 2' piece of 2X tippet. It works, but I usually reserve it for smooth bottom runs as when the lead core wraps around something it normally doesn't come out.
If I know I'm fishing bigger water like the grand in OH and plan to fish some streamers I'll put an integrated sink tip designed for the rod I'm fishing. It is just easier that way. Then I can fish that line through most any of the runs and riffles. If I want to go heavier I can always add the lead tips from above.
For most of the steelhead sinking line fishing I did, 5-6"/sec was about right. Any more and you were hung up too much. Any less and you didn't get down without additional weight. 6 ips was enough to to the head of a pool, let the line drop 3' to the bottom by mid-pool, and fish the middle and tail out. If you want to fish the head of the pool it is tougher depending on how fast the plunge is.