I’ve got a recumbent in which I can put my foot down flat on the ground with my bike still vertical, so I’ve not had to deal with tipping while remounting for years.

You may be trying to start in too high a gear—that often makes tipping more of a problem when you try to start pedaling again, because it is hard to get up to balance speed.

If you had said that you were having trouble with tipping when you stopped to put your foot down, I would have suggested that your saddle might be too high—for utility riding with a load it is useful to have a low enough saddle to put your toe on the ground without having to get off the saddle or lean the bike way over. That’s a lower saddle position than bike shops usually recommend, since it is slightly less efficient, but for touring or utility riding, the extra security of not having your bike tipping is worth the small loss of power.

My main “problem” or concern has simply sheer bulk weight of heavy groceries. I just find I can’t seem to remount my bike from stopping at a traffic intersection without the danger of tipping. So I walk across an intersection to get to a bike path.

Oh well..tiny concern.

Other awkward loads:

200 lbs of bananas for Bike-To-Work day (not a bulky load, but hard to pull up the average 4% grade to UCSC)

a 10′ ladder (lashed to the rear rack, and with a trailer lashed to the end to support the weight).

first Trail-A-Bike. It wasn’t really an awkward load by itself, but I had gone to the bike store with my son in a Burley bike trailer, so I came home with him on the Trail-A-Bike and the trailer hitched to the back of the Trail-A-Bike. Since I ride a long-wheelbase recumbent, this made for a rather long bike train.