To decide what are the pros and cons of going public or stay private, first of all we have to understand what section 302 of SOX is requiring of the CEO and CFO
Section 302 of SOX requires that a company's CEO and CFO be personally responsible for accurately reporting all materials in respect to their company's financial health and stability. Additionally, Section 302 states that the company's CEO and CFO certify that all of the proper "disclosure controls and procedures" are in place within the internal accounting functions of the business to guarantee the accuracy and timeliness in the company's financial reports released to investors and the public. Section 302 goes on to state that any willful signing of these certifications by a CEO or CFO who knows they are not accurate will result in fines up to $5 million dollars and up to 20 years in prison (Cohen & Brodsky, 2004)
Pros for Apex:
• Meeting 302 SOX requirements opens the door for Apex to go public and obtain much needed capital from outside investors should those investors choose to take a chance on Apex and place their money in their stock.
• By receiving additional funds, Apex can pursue moving into the food production markets and have a shot at greatly increasing their market share and earnings as they move through new ventures.
Cons for Apex:
• In order for Apex to meet SOX 302 compliance, the company's directors and officers (D&O) insurance policies will likely increase substantially. According to research of public companies meeting 302, strong companies saw an increase in premiums of 25-30% where smaller and weaker companies saw increases of as much as 400% in their D&O premiums (Cohen & Brodsky, 2004).
• According to the Wall Street Journal, companies seeking compliance with 302 can expect annual increases of 25% to their overall accounting costs (Cohen & Brodsky, 2004).
• Continued weakness in the markets for the past 5 years has greatly reduced the amount of investors willing to take risks on new companies. Therefore, Apex could spend millions to meet compliance with their already slim margins only to find they are not able to capture the interest of investors to substantiate and offset these costs and give them enough cash inflow to move into new territories (Richman & Richman, 2013).
Therefore, the risk and the rewards for Apex must be carefully measured. In this case, it seems that Apex is on a collision course with failure if they remain private due to being cash constrained which limits their ability to obtain the equipment and substrates necessary to move to food production. However, the costs of meeting SOX 302 requirements and the lack of a firm guarantee on investors activity is concerning. There is some comfort to be found in the fact that the company has already made the commitments necessary internally to meet the SOX 404 internal controls requirements, therefore, it may not be that substantial of a cost to add 302 compliance.
My recommendation to Apex would be to do a cost benefit analysis comparing what it would cost to achieve and then maintain 302 compliance and what the anticipated cash gains would be from going public against the costs of staying private and spending that same capital on potential restructuring efforts or new product launches or obtaining some other types of private financing to remove the SOX burdens.
Once the cost analysis has been compared, it should point the team in a clear direction and help Apex make a good decision.
References:

Bartlett, I. P. (2009). Going Private but Staying Public: Reexamining the Effect of Sarbanes- Oxley on Firms' Going-private Decisions.
The US Sarbanes-Oxley Act of 2002: What audit committees of non-US issuers need to know. International Journal Of Disclosure & Governance, 1(4), 313-323.
Richman, V., & Richman, A. (2013). A Tale of Two Perspectives: Regulation versus Self Regulation. A Financial Reporting Approach (from Sarbanes-Oxley) for Research Ethics.
Science & Engineering Ethics, 18(2), 241-246. doi:10.1007/s11948-011-9260-8
Stephens, N. (2009). Corporate governance quality and internal control reporting under SOX Section 302. Available at SSRN 1313339.