Turntable Leveling, Again

If the readings are non-level in the center and level on the edges is there any possibility that the piece of wood is slightly warped?

That's exactly what I was thinking...I may have to rethink my shelf. It's bizarre...it seems like I check it, rotate it 180 degrees, rotate it again back where it was the first time, and it's not even close to the same measurement!

Try using a "bulls-eye" level. This has a clear dome showing the level for the entire 360 degree range instantaneously , and will make leveling a shelf (or a turntable) MUCH easier!

While it is important that the turntable be level, how level it has to be depends on what kind of table and arm and what some poeple consider perfectly level.
First off, the most important reason a turntable should be level has to do with the balance of the arm. If the arm is not level, the balances will change slightly, and the less out of level it is, the less it is affected. It is also important the arm be level in relation to the platter, so the alignment does not change according to where on the record it is, and it is important that on a table with a suspension, that it not lean one way or the other so as to change the behavior of the suspension.
Not being totally familiar with the sl-1800 you are having problems with, I will offer this, it could be that dependind on what type of suspension it has, where you place the level could be having an effect on the turntable because of the weight of the level, or you could be getting different readings because the platter or mat is cupped, which some are to better support the record, or your level is not accurate, which is confusing you.
Being a carpenter, I will point out that almost all levels made today are not true. Proper leveling technique is to get the same reading when you flip the level 180 degrees, then you eliminate all variables. In other words, If the bubble is dead center and then you flip the level end to end, and it is not also dead center, your level is out. If the bubble reads slightly to the left, when you flip the level end to end it should read slightly to the right the same amount. That is how to level using a level that is off, and also how to check if a level is accurate before you buy it. It is not really nessessary to have a level that is totally accurate, but one that is easy to read.
I should think that the sl-1800 does not have a separate suspension separating the platter and arm from the table? How springy are the feet? If you are fairly confident that it is stiff enough to not change level by placing a level on it, I would say leveling the table itself is going to be close enough.
Hope this helps.

Do you mean the little $2 Sears circular level, or something else altogether?