Large companies can identify innovators, or at least learn to do so. In some cases, it will be as obvious as the founders of companies they've acquired. In other cases, it may be simply polling the engineering and product management ranks and tracking down those who are considered innovative by their peers. Or, you may even make it egalitarian and offer developers a 'year of invention' after some number of years at the company.
One point I think is key is to create an environment that is conducive to innovation. Relaxed administrative obligations, flat organization structure and a budget. Nominal oversight and justification requirements. Then, a simple guideline: What is developed needs to be on a path to becoming a product or service the company could offer.
Innovators could be supported with HR for finding contractors or consultants to work with, purchasing for buying components or equipment, marketing and business development persons could be assigned to the program to help innovators with business plans, cost and pricing analysis, market research. The innovation organization could be placed in a work space with dedicated space for their project, and a common space to meet and collaborate with other innovators.
Rewards for successful products could simply be additional stock grants and recognition, or perhaps simply another tour of innovation.
The risks would be if the program were abused and budget misspent, or the innovator simply didn't do any real work, or went off the rails with their projects. Also, development projects could have many budget sizes from virtually nothing to multiple millions. Perhaps the business development partner could help with proposals to request additional budget, once prototypes were far enough along to be compelling.
A multi-billion corporation could easily allocate a few million to this type of environment and keep a dozen or so innovators busy. You'd only need one success every so often to make it worthwhile.