Well, it has actually been quite some time since I originally asked this question. With that said, I will report back on what I ultimately ended up doing.
Instead of a cart, I bought an apron that has four pockets across the front. In the apron I have my twist tie labels, my baggies, a marker pen, retractable slim-line box knife (essentially a skinny razor blade), tweezers, and q-tips. I have a tray I carry with me that holds small dixie cups(the paper ones with no seam along the bottom) fitted in to a custom styrofoam insert I made to keep them from tipping over. I can fit 20 cups in the tray at one time. A clipboard (with a pen on a chain…LOL)for documenting my crosses also sits in the tray on top of the cups.
I use baggies to protect my crosses from rain. I prep the baggies in the boring winter months (usually while watching TV…LOL) by cutting the corners off for ventilation and storing them in a used tissue box for easy access later. I make my crosses using the q-tips for pollen application (can’t use my fingertips…my long nails get in the way…LOL). One q-tip per pollination (or pollen donor)and they are disposed of afterward.
So, in the end, I went a much simpler route. I do occasionally carry a light “bar” stool in to the garden to set my tray on while I am doing everything in a particular area. My garden is basically flat and the stool puts the tray at almost waist height, which is a nice convenience. The stool usually sits with my potting bench so it is easy access to grab and put away since I gather and replace all my supplies from the potting bench anyway.
The process is simple and fairly quick this way while still giving me the convenience I was looking for. The apron was really the key and then the customized tray.