I understand your situation, but it's important to note that the message limit of 40 messages per 3 hours for GPT-4 is set by OpenAI to ensure fair usage and system performance for all users. This limit is dynamically adjusted depending on demand and system performance in practice source (https://help.openai.com/en/articles/7102672-how-can-i-access-gpt-4).
Attempting to circumvent this limit with an autohotkey script or similar could potentially violate OpenAI's usage policies. It's recommended to use the service within the set limits and guidelines.
If you find yourself frequently hitting the message limit, you might want to consider optimizing how you use the service. For example, you could try to batch your requests or make your interactions with the model more efficient.
Remember, the model can only accept and understand a small amount of data at once, about 2000 words, measured as tokens. You must find a way to use your data in small batches source (https://community.openai.com/t/399797).
If you're using GPT-4 for academic purposes, you might want to consider reaching out to OpenAI directly to discuss your use case. They may be able to provide further guidance or potential solutions.
Note: you can ask me a follow up question by @ mentioning me again :speech_balloon: