Automotive Speedlight Softbox Recommendations and light increase?

I currently have a 430EXII and two YN560's.... These light up Motorcycles etc perfectly however get hotspots barebulbed depending on the subject (chrome,etc.) and sometimes give a harsh shadows to model. I was curious what would be reccommended for softboxes for this coverage or should I stick to shoot-thru umbrellas? I could do barebulb on the sides with a softbox for the main? Also I was thinking about adding three more YN's to double head for two reasons: more light at full and when full is not needed faster readiness. I shoot mostly anything with wheels and want portability. Not sure with the light output if I should save for AB's for example but would be way out of budget for some time. Thanks....

Lighting large objects well requires large modifiers.
While a speedlite might fill the modifier, it will not be delivering much light to the subject.
So, it comes down to what you want to accomplish and how much budget you have available.
Also, the shooting style and processing you want to achieve.

One approach is multiple exposures with camera locked in position on a tripod. Then blending in processing. You will get more light per dollar with moonlights. AB800 is 320 Ws, Einstein E640 is 640 Ws. With VML they are both portable for the kind of shooting you want to accomplish.

To some extend you have to accept that there will be specular highlights from light sources when shooting chrome and polished paint. Being careful with angles helps but the rest has to be taken care of when processing the image(s). For example moving the light for multiple shots and then blending to eliminate each hot spot.

The problem with using bigger modifiers for automobile use is that larger modifiers equal larger reflections. It may or may not work for a given application. One option to consider is using a softer light on your model, and bare flashes on the vehicle where shadow transitions are less of an issue. There is an auto lighting setup thread on this forum.

And there is an F Stopper video where a commercial photographer lights a high end sports car. I think his setup required about a dozen heads with several power packs and a 30 foot soft box from Chimera.