I submerge the print by sliding it quickly into the developer and then agitating using rubber-tipped print tongs (I have bamboo tongs that have been going for 20+ years!). A side or end of the print floats up in the developer and I gently press it down with the tongs. Moving from area to area doing this throughout the entire developing time provides constant and even agitation. Often, I'll flip the print face down for a bit and then face up again. I'll use two tongs for larger prints, but manage 16x20 usually with only one. The tongs allow me to handle the prints all the way through the fixer without contaminating my hands. Never damage to the paper surface this way either.
When developing more than one print at a time, I use my hands and shuffle the prints. I do not use gloves for common HQ and PQ developers, but do for amidol and glycin developers (and for pyro negative developers). When shuffling, I often get some emulsion flaking on the very edges of the print where I handle the paper. For me this is not an issue, since I print with generous borders and trim them off when mounting. When I shuffle prints, I am careful to wash and thoroughly dry my hands before returning to the dry side for more enlarging.
I find tray rocking inadequate for agitation personally, but there are those who have mastered the technique of setting up enough waves in the solution to do the job. I've simply never found it necessary. I have not had problems with print damage from tongs or fingers ever.
As for developing time: Your 1'40" is much to short for optimum development of most fiber-base papers. That, coupled with your possibly inadequate agitation is likely the cause of your density variations (although, it could also be enlarger-light fluctuations, especially if you are using a cold-light head).
I use 2.5 to 3 minutes as a starting point for fiber-base papers and often develop for up to 5 minutes. Try the three-minute developing time recommended above, increase your agitation (more can't hurt!) and see if that eliminates your variation problem.