It sounds like you have a boat which is very similar to mine. If I remember right mine doesn't give a specific name on that same tag either, it just says 850E. I looked through a bunch of the models for 1979 and 1980 on
this site but I didn't find an exact match. However, the only model that used "850" in its designation was the "Supreme BR" so I'm going to guess that the "BR" stands for bow rider and that the boat is a Supreme. I never measured my boat but it has been in my family for 25 years and it is supposedly 18.5 feet long which also makes it sound like its a Supreme. I agree that a swim platform on the back would be very nice, my 6 year old daughter is like a fish too. I just got done rebuilding seat bases for the first time and the rest of the seat panels for the second time. This time I made sure to get pressure treated plywood and use stainless or galvanized fasteners throughout so hopefully I won't be doing it again for quite some time. Mine has the original 200hp, 305 cubic inch, V-8 Chevy in it, I'm hoping to build a 350 for it in the next year or two to give it a little more oomph. Its not the best on gas but its not terrible if I keep it under 3000rpm, its gotten worse since I put a Weiand aluminum intake and an Edelbrock 4 barrell on but as long as I keep it on the primaries its OK. I also have the twin 18 gallon tanks under the seats, the mounting tabs had been cracked for years and one even broke off, luckily I have a friend that TIG welds and he did them over better than new. Mine has a sun-deck in the back instead of seats next to the engine, I've never seen another one around with the sun deck. There are still quite a few of them running around on Greenwood Lake where I live. I can think of 4 or 5 off the top of my head that I see regularly. I've got mine out of the water this week in preparation for a trip to Lake Wallenpaupack this coming weekend with the family. Now that the weather has cooled down and the boat is out anyway I'm going over the exterior with a buffer and I'll post some pics of it when I get done (hopefully tomorrow if the weather cooperates). What I'd really like to find is a reproduction of the original decal for the side, mine were pretty hammered and I peeled all the decals off rather than have chewed up ones on there. I'm going to talk to a guy I know that does vinyl, he may be able to make them up but probably only in once color to keep costs down.
By the way, where are you located Mike?
John