Navigating the labyrinth of well drilling companies in Maine can initially appear as an arduous task, yet with a strategic approach, the experience can be likened to a systematic scientific experiment, underpinned by the principles of rational choice theory. In this pursuit of securing the optimal well drilling company, an array of critical questions emerges, which, once resolved, significantly refine the decision-making process. Allow us to delve into these questions and unravel their relevancy to your search.

First, it is crucial to question the longevity of the company in the well drilling industry. This is not a mere matter of curiosity, but it ties directly into the concept of survivorship bias, a bias that can easily taint our perception of a company's competence. Companies with an extensive track record have weathered the tumultuous storms of economic downturns, technological changes, and increasing competition. Their sustained existence can often be attributed to adaptive capabilities, proficient expertise, and robust client relationships.

Secondly, you must query the company's knowledge of local geology. Maine's geology is a mosaic of varying rock types, aquifer depths, and water quality that can drastically impact the drilling process. The significance of this knowledge is underpinned by Bayesian statistics, where prior knowledge about conditions greatly improves the prediction accuracy. Therefore, companies with a profound understanding of local geology can not only predict potential challenges but also devise effective solutions, thus eliminating unnecessary costs and time delays.

Thirdly, interrogate the company about the technologies and methodologies they employ. Modern well drilling techniques range from traditional rotary drilling to advanced sonic drilling. While rotary drilling is a tried-and-tested method with broad applicability, sonic drilling is faster, provides cleaner samples, and reduces waste. However, it's pricier and requires more expertise. This trade-off invokes the economic concept of cost-benefit analysis. It would be prudent to select a company whose technology aligns with your project's unique requirements and budget constraints.

Fourthly, pinpoint their licensing and insurance details. The significance of this query is echoed in contract theory, which underscores the importance of protection against potential breach, accident, or negligence. Licenses validate a company's adherence to state regulations and industry standards, while insurance mitigates potential financial risk. Hence, companies lacking in either should be approached with caution.

Lastly, investigate their post-drilling services. While the initial drilling is a significant part of the process, maintenance, repairs, and potential expansion should not be overlooked - reminiscent of the iceberg theory. Companies offering comprehensive post-drilling services ensure the ongoing performance and longevity of the well.

However, it is essential to remember the Pareto principle in this exploration. It is likely that 20% of the prospective companies will fulfill 80% of your requirements. Therefore, your goal should not be to seek perfection but to identify a company that best aligns with your specific needs.

In conclusion, the selection of a well-drilling company in Maine may appear daunting, but with the right questions guided by principles from various intellectual fields, it can become a logical, informed process. Remember, your well is not just a source of water, but a long-term investment. Therefore, taking the time to execute due diligence in your selection process is undoubtedly time well spent.