I am trying to figure out a good way to secure my feet to pedals of my new hybrid bike.
Plenty of ways of doing that. The overall most common are the SPD-style "clipless" in a variety of models.
I don't want to use cleats for a number of reasons.
Any time you want to achieve a certain goal w/o using the most common method, expect to struggle.
I am not looking to have them 'locked in'...
I think youre overestimating the minimum retention force that can be achieved.
.. just a way that I don't have to worry about my foot slipping off if I'm going downhill at 30mph.... I'm doing a lot of urban riding right now...
Keeping your feet on the pedals while riding on proper roads should not take much. Even the most basic of platform pedals with a metal cage ought to be able to do that.
In the past I have used toe clips with straps, but I would like something that would be a little quicker getting my feet in and out.
So try the "power grips" as favored by many fixie riders.
I have tried some strapless toe clips, but they don't fit my running shoes at all.
Well, running shoes are not very good as cycling shoes whichever way you look at it.
The sole is too wide and too soft. A stiffer sole overall is generally recommended for more dedicated riding.
And the strapless toe clips are more about providing a way of pulling at the pedal than they are about keeping the foot firmly planted.
So, you don't want to use the most common method, but you do want to use a shoe poorly suited for the activity.
Your odds of finding a good solution have just been further reduced.
So does anyone have any ideas?
Power Grips:
http://www.powergrips.com/
Are there 'grabby' pedals that would work with normal running shoes?
There is the style favored by the DH/BMX crowd. Wide platform pedals with replaceable studs/pins that sink into the sole:
https://www.outdoorgearlab.com/topics/biking/best-mountain-bike-flat-pedals
Although you won't get full performance from them if you insist on riding in running shoes.
And you may shred the running shoes rather quickly.
Or a system that allows you to pretty quickly get your feet in and out of some kind of clip with a minimum of hassle?
I like Crankbrothers SPD-style pedals.
They're not the most long-lasting, but the retention force, float and ease of entry suits me.
MTB-style cleats do have a learning curve.
While some claim otherwise, I do believe that there are only two categories of SPD riders, those that already have fallen by failing to unclip, and those that will fall due to failing to unclip.
Usually, it's a slow topple. Unless you land in a bad spot, your ego and pride will suffer more than your body.
So lean up against a handy wall, lamp post or anything, and do a session of unclip training. Swipe your heel out at the bottom of the stroke. Within minutes, you'll be ready to ride. Within hours it'll feel perfectly normal. Within days, it'll be second nature.
You might not like the first make& model you try.
But there is considerable tunability available. They come with different degrees of "float" and retention force.
And ways of tuning that retention force.
Sometimes by turning a screw to adjust spring tension, sometimes by using different types of cleats.
I've even seen ads about a magnet-based shoe retention system. No personal experience though.