I would go with a modular approach to bags, and yes, the 'old lady groocery trolly' is very vialbe. As light as you think you will pack, the gear gets heavy fast when you are carrying it on one arm, even with a shoulder strap.
I use a steel skinned over light wood panels case, that my Mamiya C-330f originally shipped in. It holds my heads, battery packs, triggers, flash meter, cords, fash head backets, speed rings, gaf tape, etc, and is semi-often accessed while the shoot is progressing. The inside lid has a semi-permanent list tacked in to aid in reminding you what to pack, and what to check, like batteys for trigger, for heads, etc.
My stands and reflectors/softboxes/flags and blackout cloth live in a big nylon over rigid closed cell foam long flight/road case. A hockey bag/army surplus duffel bag would work well here also. My bag is sized to also hold a fold up stool, and tripod. Once the gear from this bag is up, it gets bungee corded off of a stand with rocks, etc added to wiegh a stand with a large modifier on it.
I use a hand trolley, with the grocery cart would work well for a less rigid bag.