Most prop trading firms use Section 475 MTM accounting on securities trading, which is business ordinary gain or loss treatment. That's not good for people with material capital loss carryovers, since you can't offset ordinary income with capital losses, except for the once per year 3k capital loss limitation. You need a prop firm to pass through capital gains income instead, or generate it from futures or retail trading.
What does it matter if the retail losses were incurred in the same year? You would have needed to elect MTM before April of that year to convert the losses to offset with the K-1, yes?
Most prop trading firms use section 475 MTM ordinary gain treatment on trading gains, and tax treatment is passed through on a Schedule K-1 to LLC member prop traders. In that case, you are out of luck if you have material capital loss carryovers, because you can only use them up against capital gains, with a capital loss against ordinary income limited to 3k per year. There are only a few securities prop trading firms who skip Section 475 MTM and use capital gains and loss treatment. Try to use up capital losses with retail trading if allowed by your firm, or in futures or forex with a capital gains election. Investments, too.