Mudbug, Here's what I do. I use Barge contact cement and Barge thinner exclusively, and because I use quite a lot I buy in gallon lots. Many years ago I bit the bullet and bought one of those "high-priced" Teflon glue pots. One of my best investments and decision ever.
I use my cement probably much thinner than everyone else, and I can mix it right in the glue pot. I like my cement about the consistency of thin pancake syrup. It will actually run off the brush as opposed drip when I hold the brush over the pot. The better quality brush along with the thinner cement allows me to be much more precise with the placement especially in tight areas. Because it is thinner I use two coats to insure a really good bond. First coat penetrates the fibers and when that glazes over the second coat goes on and when that glazes it's ready to join the pieces for a really good bond.
Invariably there will be some errant cement getting into or onto an area where you don't want it. Take a paper towel, Scott shop towel, or whatever and put some Barge thinner on it and wipe the cement off. If you do it thoroughly the cement you did not want just goes away. Please be very sure you are thorough with your cleaning because just a tiny bit of residue will be a resist to dyes, and other finishes.
Now to address your other question, I can't really comment on alternative cements, because I've never used anything but Barge in many, many years. I have been told that Original Weldwood brand contact cement works very much like Barge. The others you mentioned I have not tried, but logic makes me believe they would be just as prone to being messy as Barge and probably very similar in difficulty cleaning.
I think the THINNER cement and relatively quick and thorough cleaning with Barge thinner could go along way to solving your problem.
(The thinner will also remove the cement from your hands and it even leaves the skin!)