Wheel gap doesn't have much to do with it - the bounciness is related to the dampers and springs. The stock suspension has too soft of springs and dampers that aren't powerful enough. This is exacerbated with non-RFT tires because the RFT tires add noticeable spring rate(stiff sidewall); take those away and the car feels softer than ever, because it is.
Lowering the car will result in a stiffer ride regardless of the path you choose because there's less suspension travel available - so the car has to move less. Bumps will be more abrupt.
Rolling diameter of 16", 17", 18", 19" wheels ... all the same on our cars when the tire height is factored in, so that doesn't have anything to do with the ride height.
I'd stick to a height-adjustable kit for the reason that it's height adjustable. KW V1 is the popular choice. Perhaps TC Kline has something in your price range (which you didn't specify), they will certainly provide better ride quality and handling than KW.
2011 BMW E92 335i, 6MT, M Sport, Le Mans blue - Michelin PSS, Quaife LSD, JRZ RS Pro, JRZ camber plates, Eibach ERS, full M3 susp, custom toe arms, Powergrid end-links, brake ducting, SS brake lines, UUC SSK, ETS FMIC, ER CP, Perf. Exhaust, work by VAC Motorsports in Philly