I am wearing the business-owner hat to answer your queries with these assumptions:
1. The training you are conducting is aftersales training.
2. You know your products well and are doing a great job at these training sessions (your strength).
3. You love your job and the company (you want to save costs for the company) (company's strength - high employee engagement as employees are willing to go the extra mile).
Since this is a reputed company (company's strength), hiring based on assignments may not be aligned with the company's branding strategy. A full-time staff is readily and easily deployed to meet clients' needs compared to someone who is on an assignment basis, and engagement may be based on a first-come-first-serve basis. As this is product training, you may be prohibited from taking on similar assignments with other companies due to confidentiality issues and competition clauses.
As I am a practicing Positive Psychology consultant (which is about a strength-based approach), my suggestion is to leverage the current strengths (as highlighted above) to achieve an outcome that is a win-win for the company and yourself.
In addition to conducting aftersales training, work with your sales & marketing department to create sharing workshops for clients. These workshops should not be laden with a sales pitch but with the objective of creating awareness and knowledge sharing of a cause (in this case, e-learning). You can share about trends in e-learning; pros & cons of e-learning; research surveys on e-learning, etc. You can also invite some of your satisfied clients that have implemented e-learning to share about their experiences (the best sales generator).
The marketing team can customize and send out eDMs to schools inviting them to attend the workshop; you get to conduct these workshops, and when the attendees are impressed with your knowledge and consider you an expert in the area, they will come back to your company to inquire more or buy your products and services. Once they buy your company's products & services, this translates to increased sales; your aftersales training will increase, and you will be so occupied that you won't even have time to worry about wasting the company's money and being idle most of the time.
Hope this is helpful and have a positive week ahead!
Regards,
Autumn Jane