Here are some ideas I use and have used, some of them, related to bike commuting.
1) One shoulder strap per item, many items
I often carry a couple of lunch bags, a backpack and "a large purse", not by bike, but a short distance to and from a car. The lunch bags have a single but long and regulable shoulder strap. I use then over the shoulder and under the opposite arm, that is, the strap crosses my chest diagonally. Since they are two, I put one on each side, so the straps form an "X" in front of me. The items are removed in the opposite order they where put, otherwise the straps get tangled.
This allows me to easily walk with three items, I could carry more lunch bags this way, it's easy enough. The only cumbersome item is the large purse. It only as two long hand straps, but not long enough to comfortably carry on the shoulder.
Carrying 3 lunch bags:
I'd try to adapt this technique to your situation. I guess the bags you have do not already have shoulder straps. But maybe they have eyelets or rings for the purpose of attaching removable ones. You may be able to purchase removable, length adjustable shoulder straps and sew rings on your bags to attach them.
There are some dog leashes that already have a convenient locking hook on one side and it is easy enough to sew or tie another hook on the other end; I source the hooks on local hardware stores. (they would not be length adjustable though).
Dog leash hook:
An alternative to removable is to directly sew a strap to the bags, but then, provide a convenient elastic loop or something to tuck away the straps so they are not flopping dangerously when riding.
You can also make only one side removable, leaving the fixed side near the point where a zipper starts to open, so you detach one side, put the strap inside the back and zip it close.
2) Single strap loop threaded trough many items' handles Another technique I use to carry several items is to form a loop with the dog leash, after threading it trough the handle of the items (like many small supermarket bags). If I manage to get the correct loop length and the combined weight of the items is not too much, I can comfortably carry it for the 10 minute walk from the car to the apartment.
3) Giant or really large backpack A relative of mine has a big backpack that is only one compartment and one opening. Since it is so simple, it can be rolled compactly when empty. One of such can be convenient for your situation, since most saddle, frame and handlebar bags ase usually much smaller than panniers, maybe you can easily toss them inside a large backpack and when returning to the bike, you roll it and store inside one of the other bags or strap it to the frame. This solution can also be very useful when running multiple short errands, since the backpack would be already "attached" to you, you only have to stop, lock bike, do errand, return to bike, unlock, ride, repeat.
In this line of thought, Another idea that may work for you, is to add 2 straps to one of your bags, so you can use it as a backpack when off the bike, and attach the other bags to it. (I guess your bags attach to the bike with many short velcro straps and loops, just tie them one to another)
Personally, for commuting I preferred a backpack, precisely for ease of removal (or not needing to) for running errands. For longer commutes I had an open basket on a rear rack and I tied the backpack with an elastic strap to keep it from being stolen during a stop or red light. For some time I also had a lunch bag adapted as a handlebar bag. It was quick to remove and I carried it crossing the strap around my chest.