What can I do about getting my sample through the queue and my data as fast as possible?

Make the best library you can! Build a good, tightly-sized, clean library and share information with us about any residual linkers, primer sequences, barcodes, UMIs, adapters, polyA stretches, normalization controls, even the results of your test sequencing of the Topo clones can be helpful. Getting through the queue fast is dependent on passing the Core's QC. When libraries don't sequence well, they end up getting reworked and rerun, which translates to more expense for the investigator and longer queue times.
Other than that, we are a first-come, first-serve facility. We cannot prioritize your sample ahead of others.
The guidelines for library construction and validation are there to ensure good performance. The Topo cloning and pre-sequencing is important to determine whether the linkers, adapters, sequence priming site, and attachment sequences are in place. The sizing guidelines are extremely important. If your sample covers a wide size range, it's better to make several size cuts and turn in several sub-libraries.
If a user needs to analyze an inordinate number of samples which would set back everyone else, we will work with them to create a schedule that does not negatively impact the other users. (So if you have 120 samples, email us in advance please. This will also give us as much notice as possible so we can have the reagents in stock and will be ready to get them moving as soon as they arrive).