If this is such a big deal for you then perhaps blacksmithing is not an appropriate metalworking craft for you.  Home shop machining would suit your proclivities much more closely!

Bondo, if two pages of replies by experienced smiths in this thread telling you to leave the anvil alone and work with it as it doesn't soak in, then Thomas' previous comment should seriously be taken to heart.

Had to find my notes: the last time I was in Peter Ross' shop for a NCABANA meeting, he stated that the most useful feature of his anvil was the 1/16" of sway from end to end, as well as side to side.

I don't know squat about smithing , as I am pretty much brand new as well.  However, I learned long ago that when I ask a group of folks that have experience measured in decades telling me to do A but I still go and do B, I am pretty sure whatever decision I made was the wrong one.  Just saying...