From my experience, soaker hoses and drip irrigation is not a good fit for rainwater, especially not gravity fed rainwater.
The main problem is, even with a good roof washer, you end up with a lot of silt, dust, grit, etc. in the water and this tends to plug up drippers, small holes, etc. You could run the water through a filter, but that requires pressure, which you don't have, or really large filter surfaces.
One possible option would be to make a water tower that is fed by a small pump (perhaps powered by a solar panel) from your set of barrels, You could tank a plastic barrel and disguise it as an old style wooden tower, that might appeal to your wife's aesthetics.
Another option would be to run a small pressure tank and pump, but that requires more power.
If you are watering larger, fixed plants, like trees/shrubs, then you might try using 'bubblers', they are less likely to get plugged up and will work well with practically zero pressure, but tuning them so they all produce the same amount of water is tricky and time consuming.
Finally, there is always the manual option (our primary way of watering with rainwater), i.e. buckets, or a hose that you move from plant to plant.
Note: Most people are in business to make money. Just because they sell something they call a 'rain barrel soaker hose" doesn't mean that it works well in that application. Google "Laundry balls" as an example of something once sold that the sellers KNEW didn't work.