Here's how capital gains are totaled:
Long and Short Term. Capital gains and losses are either long-term or
short-term. It depends on how long the taxpayer holds the property. If
the taxpayer holds it for one year or less, the gain or loss is
Net Capital Gain. If a taxpayer’s long-term gains are more than their
long-term losses, the difference between the two is a net long-term
capital gain. If the net long-term capital gain is more than the net
short-term capital loss, the taxpayer has a net capital gain.
So your net long-term gains (from all investments, through all brokers) are offset by any net short-term loss. Short term gains are taxed separately at a higher rate.
I'm trying to avoid realizing a long term capital gain, but at the same time trade the stock.
If you close in the next year, one of two things will happen - either the stock will go down, and you'll have short-term gains on the short, or the stock will go up, and you'll have short-term losses on the short that will offset the gains on the stock. So I don;t see how it reduces your tax liability. At best it defers it.