... sound batting and/or weighting speakers ...

To whom it may concern; I mean no disdain in my comments. Here's the deal; I spend a LOT of time around here watching people recommend spending money on upgrades. As if money grows on trees. Sure, big improvements can be had.... if you have big money to spend AND the time and inclination and ability to shop and compare. Even then however economic profit considerations will always limit design leaving lots of areas of improvement. These can be found all over the place, from speaker gaskets that seal but don't control vibrations to diodes and caps that are cheap and hold back performance. Because of all this the spectrum of performance manufacturers leave on the table is HUGE! There are many, many significant performance improvements that can be attained at little cost. The legs of the ladder are endless. 

So, keep reaching! Make a change! Go for not just one tweak, but many, for a far superior sound. :)

Physical, operational limitations on designs cannot be escaped through tweaking, weights, etc.

 A box is a box whether it costs 100 bucks or 10000 bucks. 

with all due respect, that is a completely ignorant statement from one of the self proclaimed greatest speaker designers / builders of all time, who’s actually never done either 😀

Some boxes are square, some are rectangle, some are trapezoidal, some have extremely thick baffles, some are designed to resonate (harbeth) some are made out of mdf, others hdf, others carbon fiber, some have ports, others do not. Some boxes are incredibly well braced (look at ls50’s), some have curved front baffles, some have narrow front baffles, some speakers are designed to work well with wide front baffles, some use special glue to hold them together (dynaudio), some are lock mitered.
Shoot, there are even differences with regards to the construction of cardboard boxes!

With regards to the original post and the original question, I’ve asked the same question before and was informed bracing, and cross bracing, the inside of the cabinet will yield the best results to combat the problem which you describe!  
Douglas makes a good point in that your time, money and effort might be better spent moving up in speakers.  If you like the Kef q1’s, look for some kef xq1’s or anything in the kef xq series.  I’ve had 2 pairs of xq(‘s and they are lovely speakers. Coincentric design with a super tweeter pulled straight from their reference series , curved boxes to reduce internal standing waves, and extremely well braced inside.

I sold my last pair of xq5’s for $600...