Maybe the biggest problem is that the process is too centralized. Have a useful Web resource. Have access to knowledgeable people, especially at the department level in-person, local support is best. Have specialists at GCS on categories such as NIH, training grants, NSF, etc. Approvals Make it possible to get as many signatures concurrently as possible.
Tracking is also very important.
For PI security, assign each grant a unique tracking number, then put tracking system on the web. We need a fundamental review of the signature requirements. After that we need to sort out what can be handled serially, what concurrently. With an on-line system, the signers can decide which can be handled parallel. Primary responsibility for space, time, and money should be at the department level.