I did the eibach pro kit shocks and struts with my UPR springs on my 03. Drop was about 1.5" front and rear with those springs, and my ride can be stiff, and some bumps jaring, but it never feels floaty.
IDK the spring rate on the steeda sports, but I know they are a fixed spring rate, meaning they are much stiffer feeling than the stock progressive rate. Did you keep the spring isolators front and rear? If not that explains the difference in height. If you did keep the isos, than the extra drop is likely due to extra weight, like you said, but also may mean that the steeda springs don't have the proper rate for your setup.
You will never have a smooth, cushy ride, with lowering springs. The more you do to suspension to get better handling feel, etc, the more NVH and the stiffer the ride will be.
That said, I really like the Eibach shocks and struts, and they have a very nice warranty as well. Any aftermarket shock/strut combo will be better than an OE spec replacement, since the OE spec shocks/struts (like your monroes) are just not properly specced/setup to deal with lowering springs.
Have you called steeda yet to ask their recommendation? That is a good option as well.
2003 Redfire & Black V6. Full suspension, 8.8 w/ 4.10s, tuned. 4.3L stroker + turbo capable of 550 hp soon
1992 5.0 Auto Hatchback...needs wiring, interior, ...basically everything
RIP: 2015 SHO PP, 12.87 @107 1/4 mile