Just by changing BP of the TBS your TBS will still be the same size. haven't tried it myself but seams logical.
I would do it as you said. New BP, new TBS, new TB with a new name. Load from cursor, build indexes, runstats, rename. if done online and original table received changes, grab those new changes and add them to a new table. This can be done by using triggers or other methods recently discussed here.
p.s. I suspect you do have an archival process? Maybe redesign this table using new functionality that allows you to break up portion of a table into a stand alone table.