If Your Just doing early cuts and turning to cones, then You may be able to get away with hand feeding them if like recommended, You slow down the spindle and really control the feed, but when you start putting your tapers on them You would really be much better off with a variable speed power feed, so that You can better control the feed and change speeds until one of them works. Almost every time I set up to turn shafts I have to play with them, and make these adjustments before running out a batch. Sometimes the same feed speed I use one time, doesn't work the same as with a batch turned at a later time, so I have to check them just the same to be sure. I would recommend setting up with a shaft of lesser quality until you get things dialed in.
Tail stock pressure as mentioned is also another thing to be aware of. If the shaft has no movement between turns, and both ends are running true, then there is a good chance the tail stock pressure is too high, in some cases for whatever reasons unknown to me I can still pick up some run out when trying to control these things, and have noticed that with the absence of a spur driving the shaft, I can sometimes grab & release the shaft real quickly several times, allowing It to slightly spin in the center until get It rolling true. Not sure why it works but it does, of coarse with out a spur it can be thrown out of position with manual tooling, but I don't seem to have that problem with the router. There are some situations where for whatever purposes I want to face between centers using a manual tool, I have noticed that this method will sometimes allow me to use more tail stock pressure, so that it isn't thrown out of position while I'm facing.
I don't use any kind of spur drive, just a long pointed center, and I make sure that center is running as close to dead true as I can possibly get It, I mean You shouldn't be able to see any run out in It at all, and truth be told it is better to indicate it to be sure.
Like someone mentioned each machine is different, and different things help, but over time We each pick up our own little things that help us get the final result. Some of what has been mentioned and other things have worked for me while using a deluxe (Taig based), and while using different style router bits, from slot cutters to straight bits, even using a rabbiting bit. I was able to get decent results from each after some experimenting, but I do Like to use the rabbiting bit for finish cuts (Especially for matching the joint to the handle). I've been using It lately for that, and It leaves them so smooth that I can seal with virtually no sanding if I need to.