The BK7m has been discontinued by Roland but essentially gives you all the BK instrument sounds and styles, with an easy to setup Midi function. (It’s been very popular with those wishing to add new styles and sound flexibility)

The Integra is more of the sound section of a Roland Workstation in a box and includes so called super natural sounds which add sound modelling to improve realism, however it is more of a pain to setup with the limited Midi specs of most arrangers. (Korg is pretty good in this respect though)

As you seem to dislike a lot of the PA3x sounds and styles it may be cheaper to just trade it in for an instrument from another manufacture, or if you wish to stay with Korg have a look at the PA4x which is a big jump up in quality from the PA3x.

I have compared the TOTL arrangers from Yamaha and Korg fairly recently and unless your into ensemble or classic organ sounds then the PA4x is tops for realism (When compared to real instruments and players) with the T5 some way behind. (However the T6 can’t be too far away which will probably upset the mix once again)

Hope this helps

Bill