I did the mid-size and find it fine to walk on. The larger ones look nice but probably not so easy.

Greenlydia, you can work with round rocks if you stack the second layer in further than the first, and to the extent that the rocks lean, make sure they lean into the side of the bed. In effect you are not stacking the rocks on each other, but rather embedding them into the side of the bed. I personally hate the idea of glueing and mortaring rocks together as I am prone to changing my mind about things, and the rocks can always be used for a different application if they are merely propped in place, but if they have mortar all over them they are hard to dismantle, and hard to reuse. Quite aside from which, the mortar doesn't actually make the thing any stronger. It just provides a false sense of security so that most people who use it are less careful about placing rocks so that their weight holds them in place. Both types of retaining can fail, of course, but if an unmortared rock rolls out of place... well, you roll it back, or maybe you repack the section where it came from. If a mortared rock breaks out of place, well, there goes the weekend fixing that. Regarding water, my own strategy with beds surrounded by rock retaining walls is to keep the soil level in them flat, not mounded, because I don't want water running down between/inside the rocks taking away the soil that supports them. I want the water soaking in where it lands.

In my last home, on the advice of a landscape architect, we used pami pebbles for our aggregate walkway/patio and had the concrete mix tinted a medium brown-reddish color. It was a beautiful combination, especially in contrast with plant materials and a flagstone and brick accent wall. Got many compliments over the years. I didn't find it hard to walk on with bare feet because the pami pebbles are so smooth. We had our backyard patio installed a few years later by a different company and was talked out of using the same materials. Never liked the patio as much as the front yard - in looks or bare-foot comfort.

I don't know the answer to your question, sorry. I have a similar path and also have similar problems walking the lawnmower across/along the path. One thing I have which makes things slightly easier for walking is that instead of 18"x18" concrete tiles, I use larger (wider) pieces of flagstone (about 30"x18"), and I find that I can easily walk along the path because the flagstone is wide enough and appropriately placed so that I end up stepping on it, and not the pea-stone. Yes, the pea-stone is difficult to walk on, but most of the time my feet end up landing on the flagstone. However, the lawnmower is still a bit of an issue for me. I would suggest that if you can't find a solution to increase stability , you could try replacing the stepping tiles that you have with something larger similar to what I have, or put a second line of stepping tiles alongside the existing tiles. This would at least help with the walking because the stable part of the path is wider. It may also help with the lawnmower a bit because both wheels will run along the tiles for part of the time. Not a great solution, I know, but if you are stuck. Also you may find that the pea-stone over time works its way into the garden and the garden dirt, mulch works its way into the pea-stone, and then weeds start to grow in the pea-stone - you might want to consider putting something else along the edge of the path to better contain each side.