What do you do? As I teach my students early on, they are always arranging the music anyway (this is mandatory for all my students) so they 'engineer' a rest at the appropriate point. As has been said, there is no work around other than to do this or not use DSP effects.
If you're using registrations rather than editing OTS, and you're switching from one solo sound to another (or in the case of Tyros, Genos and SX instruments, changing from a solo instrument to two layered sounds, or vice versa), then make sure that you have the required voices in R1, R2 and R3 as required. Make sure that R1, say, isn't changing voices when you change registrations.
And while this issue is not confined to Yamaha arrangers, there are other makes that allow seamless sound changes, and we can only assume that 1) Yamaha are aware of the issue [given the times it's come up on forums, been mentioned in product reviews (mine included) and brought up at meetings (that I have attended), they must be aware!] and 2) there's some deep down reason within the operating system or sound generation system that prevents them from sorting it out.
One day, we'll get that all-new OS, with a new style engine and all the things we've been asking for. Trouble is, it might not be backwards compatible and then people will complain about that!