@pand1024 It's very unlikely that any kind of spawnerless mob grinder is going to work properly unless you have a very good handle on game mechanics. So you very well may be wasting your time.
I thought I had a handle on the mechanics, but apparently I was wrong. I built in the middle of a giant deep ocean biome at near build height limit and I'm still working on lighting up all of the caves underneath, but so far no real luck in getting spawns in the grinder. I forget the formula now but apparently there is a mob spawn cap within a given Minecraft world. This cap is increased for each player on a server according to the wiki article I read.
However, this doesn't seem to be the case. The mob spawn rate is much lower than I expected it to be. I didn't expect a ton of spawns, but a few every minute while I AFKed would have been better than nothing. In two days while putting on the final touches, there has been one skeleton and one spider spawn in the grinder. That's it.