What's your beef with the bottling bucket???
The problem with bottling from a primary or secondary instead of using a bottling bucket, is that since you have patiently gone and let your beer settle and clear, in order to mix the priming solution and beer effectively, you would have to stir it in the carboy which would a) kick up all that nice sediment you have patiently let fall, b) possibly oxydize the beer.
It really defeats the purpose of both a long primary/no secondary or a secondary if you have to stir up all the nice sediment you patiently waited to settle just so you can have consistent carbonation.
Your kettle should be fine, BUT how much deadspace do you have in your kettle with you ball valve? Most folks who have kettles with false bottoms still leave a lot of wort behind it seems. Or esle they have to tip still to get the last out.
With my buttling bucket and my dip tube, I leave no more than about 3 ounces behind, which means I can get about 52 to 54 bottles per 5 gallon batch.
So what is wrong with using a dedicated bottling bucket? Go to a hardware store and get a translucent or white bucket...but look for one where the 5 gallon mark falls way below the top of the bucket. Usually it will say 5 gallons at 3rd band from the top. (oh get the lid too....I totally regret not getting it when I did.)
Then get a spigot and make a dedicated bottling bucket. It really defeats the purpose of both a long primary/no secondary or a secondary if you have to stir up all the nice sediment you patiently waited to settle just so you can have consistent carbonation.
Mine is the translucent Leaktite brand 5 gallon container with the gallon and liter markings from Homedepot.
Here's a pic of mine from my bottling thread.
One of my dip tubes and what gets left behind.
You'll find a ton of good info here to make bottling easier.