You can still show your Rooster, most shows, even APA approved will consider best in breed and best in variety, even for non APA approved varieties (the breed must be recognized though).
I use to show my BLRW, I think that it helps when trying to get a new variety approved by the APA to bring these birds to shows. Once the judges start seeing birds that meet the standards and a consistent feather coloring, they are more apt to agree to enter the variety in the book. The BLW is an approved variety in most of Europe and Australia, I think it is also approved in the Bantam form but not sure.
I want to address this "out crossing notion" , bringing new genetics into your breeding flock by including a bird from the original combination of breeds that brought about the breed or variety is not only acceptable breeding behavior, but it is essential to reducing the amount of problems that inline breeding can create, especially when you have a limited supply of initial bloodline.
What happened with the BLW was simply greed. Instead of setting a standard, an then breeding back to that standard, anything with the original BLW line in it was sold as BLRW. I have seen people bring birds to shows that for all intense and purposes are Golden Laced Wyandotes, and list them as BLRW. I have also seen pictures posted to web sites like these that have the same problem. I have witnessed bird with Cochin style combs promoted, and used in breeding programs , rather than culled or made into pet birds (Cochins were used to create several of the wyandotte varsities because their body style is very similar to what you want in a Wyandotte)
If you want to see what they should look like , in the US, you can find the coloration on the bantam wyandottess.
Until breeders take the responsibility to only promote birds that meet the color and lacing standards, the standard BLW , will not be accepted into the APA.
Thats my story and I am sticking to it.