Why I did not reply... I had surprisingly never heard of the Shinko 804/805.
Looks like a good tire that is well priced. Looks like a tire that could be used for a 3-4,000 mile trip. If you don't like them, toss them.
After I saw your thread I searched for like tires.
Kenda Big Block $136
Continental TKC 80 $174
Mitas E-10 $196
Mitas E-09 $172
Mitas MC60 $196
All of these tires have similar block tread patterns except for the Mitas MC60
http://www.revzilla.com/motorcycle/mitas-mc60-getaway-tires which have a tapered pattern that can be reversed. Quieter on the road and more aggressive off-road.
Looks like most of the tires advertised 4-5,000 miles for a rear and that would depend on whether the rider wears the tire till its smooth or replaces it after the best is gone.
These tires vary in construction, weight, ease of install/removal.
So how much do you want to spend. What terrain are you going to ride? Sharp rocks might make you want thicker sidewalls.
I am a terrible off-road rider and can use as much help as possible. Recently took a trip... Eastern Sierra, Death Valley, Mesquite NV, UT, WY, MT, WY, ID, UT, NV, CA. I missed many beautiful off-road miles by not having a more aggressive tire. Should have slipped on a pair of noisy vibrating blocked tires while traveling and pulled them off after the trip. Currently running Full Bore M40 which is a good tire but nothing like a big block tire would be.
If you are in this area
http://goo.gl/maps/6Nj54 Soda Lake Road is a good location to test tires. It has very good asphalt, terrible asphalt, gravel, sand, and silt (sand that has broken down). Quatal Canyon Road is all dirt. The rest is fast and fun.