Additionally, we brought down our selling and marketing expenses by nearly 30% during the quarter by optimizing our marketing campaigns and streamlining our sales process. Turning to our third quarter and recent sales and operational highlights. In Publix, we converted from a DSD model to a direct distribution, enabling us to take more control of our distribution to drive profitable growth and lower sales prices for our consumers. Since the conversion, sales volume improvements have eclipsed 38% unit growth week-over-week. Given the positive results, we plan to leverage this model with other retail partners in the future. In August, we received authorization from Whole Foods for our Hard Ginger Ale and launched our first ever national alcohol promotional showcasing our Reed’s Hard Ginger Ale and Classic Mule.
For the 12-week period ending October 15, alcohol sales have increased over 120% year-over-year. We’re excited to continue deepening our ready-to-drink alcohol presence and look forward to generating more wins ahead. Also in October, we’ve added over 450 points of distribution to our core products with National Co-op Grocers, a business service cooperative for retail food co-ops with stores across 39 states, serve over 1.3 million customers. NCG is one of our highest velocity chains with Reed’s being the number one supplier in the beverage category. During October, we restructured our online Shopify store to enable customers to access and purchase our fan-favorite products work efficiently. As part of our Shopify relaunch strategy, we have added a monthly subscription option and thus far, the results have been extremely positive.
Although our e-commerce sales represent a small portion of our business today, we are taking the important steps to build this channel and expect to see further growth as we invest more resources in the coming year. As we mentioned on the last conference call, in July, we partnered with Somerset Cider Solutions, a leading U.K. beverage manufacturer, to produce Virgil’s soda in market in a more cost-effective manner. We began production and started distributing products in the U.K. during the third quarter. And although we are only a few months in, we are encouraged by the early results, and as this new export model enables us to be more price competitive. We are positioning REITs for further expansion overseas as we evaluate additional EU distribution partners.
A quick update on our team. In late October, we officially appointed Joann Tinnelly as Chief Financial Officer of Reed’s. Joann joined the company in 2018 and throughout her tenure has stepped into the role as interim CFO on two separate occasions. Her experience in finance and accounting for both public and private companies as well as her execution as interim CFO makes her the ideal candidate to lead our finance team. And we are all thrilled that she has accepted the role on a permanent basis. She has and will continue to be a key member of our executive team, and I look forward to working with her as we execute our growth and profitability initiatives. Given the inventory challenges faced year-to-date, we are revising our net sales guidance for 2023 to a range between $45 million and $47 million and now expect to turn cash flow positive in 2024 as we utilize cash to increase our inventory in the fourth quarter.
However, we expect to maintain our modified EBITDA profitability and exceed our guidance of realizing $6 million of operating expense reductions for the year. As I mentioned earlier, we still see additional savings opportunities and now expect to save over $8 million for the full year. Additionally, as a result of modifying the use of certain beverage ingredients, we anticipate onetime packaging inventory valuation adjustments in the fourth quarter of 2023 that will impact our gross margin for the year. Excluding these noncash accounting adjustments, we continue to expect surpassing 30% gross margin for 2023. Before wrapping up the closing remarks, Joann will cover our financial highlights for the quarter in more detail. Joann, over to you.
