Amazon has the Sun Joe Tiller Joe TJ600E 14" Electric Tiller for $125 with free shipping. Features four steel angled tines, push-button operation, 7-inch cultivating depth, 6.5-amp motor, and weighs only 17-lbs.
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6.5 amps at 110V is 715 watts. 1 watt = 0.001341hp, so that's about .96hp. My tiller has a 7hp engine on it, and barely makes it through grass into damp soil beneath it. Draw your own conclusions.
This should be fine if you're mixing damp mulch.
^ I'm not suggesting this tiller is a powerhouse but your 7HP has some engine problems if it can't even till all but very hard dry soil, though that may be the case... dry clay is hard for any but the largest tillers to cut into.
This tiller on the other hand, has limited weight to it so what you end up doing is tilling only the very top surface as it lifts the tiller upwards then after cutting down a bit it sits lower.
So, it's going to take a LONG time to till an area that isn't very soft, idieally you'd enrich the soil with compost or other organic material using a larger tiller then use a lighter duty one once the soil wasn't so compacted anymore.
These electric tillers are ok for a small job like turning dirt for a garden. Not is comparing apples and oranges between the HP ratings of a gas and electric tiller. Gas tillers have vertical shafts while electric are direct drive. Pound for pound the electric model is much more powerful albeit smaller....
Do it the old fashion way. Get a shovel.