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Can my accounting for Tax Basis differ from my broker's
No. If you didn't specify LIFO on account or sell by specifying the shares you wish sold, then the brokers method applies.  From Publication 551 Identifying stock or bonds sold.   If you can adequately identify the   shares of stock or the bonds you sold, their basis is the cost or   other basis of the particular shares of stock or bonds. If you buy and   sell securities at various times in varying quantities and you cannot   adequately identify the shares you sell, the basis of the securities   you sell is the basis of the securities you acquired first. For more   information about identifying securities you sell, see Stocks and   Bonds under Basis of Investment Property in chapter 4 of Pub. 550. The trick is to identify the stock lot prior to sale.