As you said, market and technical research is incredibly important for stakeholders' consideration. If the idea is really that "grand," then the market research should reflect that. Business presentation is also a factor, having done extensive research is absolutely necessary for making a case as to why money should be put into it. A few things that could be done are specifically aligning the project with the company's mission statement, presenting a cost optimization strategy, and potentially breaking up the project in stages.

Aligning the project with the company's mission statement is a effective strategy in initializing the project and making sure the stakeholders are amenable to the concept of the project in general. Presenting the budget as a "cost optimization" strategy implies that the PM has done extensive research into places where the COGS could be cut down. This initiates a sense of trust that stakeholders may have in the PM as well as frame the project as having had extensive research into it's budget already. Finally, breaking the project into phases with different budgets could be more manageable with finances and resources that are dedicated to it at a time.

Mitigating financial challenges requires a multifaceted approach where the focus is not only on the business case presentation but also on developing strategic and innovative financial planning. Some ways to mitigate the obstacles mentioned can be through the use of pilot studies to gather preliminary data. By doing so, the project scope can be refined and may attract early-stage investors based on the results provided. Moreover, smaller and more manageable phases of investment should be focused on which would reduce upfront financial commitment and provide early indicators of the project's viability. 

Project charters, especially in front-end research and development, are difficult to secure, especially when financial models fail to win sponsor support. Based on the insightful viewpoints offered, solving these difficulties requires a diversified approach beyond business case presentations. Aligning the project with the company's mission statement emphasizes how it supports organizational goals and values. This pleases stakeholders and reinforces the project's strategic goals. Presenting the budget as a "cost optimization" approach highlights the PM's extensive cost-cutting and efficiency-boosting research. This method builds stakeholder trust and presents the project as a well-planned investment.

As suggested, splitting the project into manageable parts reduces financial risks and uncertainties. Iterative pilot studies can gather preliminary data and refine project scope depending on early-stage observations. This saves upfront costs and proves the project's feasibility and ROI. Focusing on smaller investment phases allows stakeholders to incrementally assess project viability and make adjustments and optimizations.

Strategic alignment, innovative financial planning, and phased implementation are needed to write a compelling project charter. These tactics help project managers overcome financial problems and gain the resources needed for successful R&D projects.