Why don't you want to do stepping stones? Understanding why might help us have an alternative.

Is there any way you can add a foot path? Two of my long borders have narrow (too narrow really once summer is here) paths behind them. Another large bed is split by narrow walkways from front to back every six feet or so. A lady near me put a meandering path through the middle of one of her large beds, it's hardly noticeable in the summer. Her's is more of a collection of stones, mine are mulch paths.

I use bricks in my two front beds, they blend in pretty well. (That would be because I have lots of clay.) Unfortunately, they also sink into the soil. I have to either add another brick on top of the first or attempt to make them more stable with pebbles/sand. I find that the bricks are small enough that they don't interfere with most plants and they are uniform enough that I know what my foot is reaching for.

One of my first beds had stones plopped here and there, with nothing to really connect them. What a nightmare! Once everything started growing, I looked like I was playing Twister. So if you do resort to stepping stones, be aware of what is growing between them.

One of my raised beds is an island round one, looking like a roof of a dome. Placing stepping stones there would be a pain, since they would constantly "sink", and require lifting. Visually it would not bother me, since in a summer time it looks like a cottage garden - very full, and totally covered the stones. It just looks funny in winter.
On my other beds (rectangular ones) I can place "snake" paths. I guess my main concern is "sinkiness" of the stones, and I thought there might be a better way, since the level of the soil is rather high.
I will wait till spring to do that, since all my beds are stuffed (pregnant?) with bulbs that are due this spring.

How about mulch paths?

Just flatten the area where you want to walk (you may have to remove some soil), & cover it with mulch.

As it wears down, add more.

I always wonder about this, too. So far I just try to step carefully in pretty much the same pattern and not go in any oftener than necessary.

i have found that using rock dust under stepping stones solves the sinking problem. in fact, i had a rock dust path for a year that did not sink while i worked out stone details. it settles nicely, doesn't roll away, etc. i have also used it under mulch for a mulched path.

Thank you all for great advice!
~Natalie