Hi Charlie. I don't know where you're at in terms of your level of experience, but off the top of my head, here's what I'd suggest:
Volunteer. Don't sit on the sidelines and wait to be assigned tasks that might align with what you're interested in. Put your hand up for performing tasks and techniques that are beyond your comfort zone. If you're in a meeting and it's going nowhere, take the initiative to stand up, walk over to the whiteboard, and help facilitate the conversation with visuals. The more involved you get, the less you'll feel like you're taking credit for someone else's work when you're writing up this project for your portfolio (and the more you'll learn and grow!).
Be a champion. I don't just mean "be awesome"; I mean do your best to influence the project plan in terms of involving users and following a process that is going to validate that what you're designing is going to resonate with the people who will be using it. The other factor here is making sure the rest of your team is on board with such an approach, and that they understand that UX is everyone's responsibility, not just "the UX team". It may be wise to purchase a couple of copies of some key books (e.g. JJG or Lean UX) and encouraging your team to read them, so they get where you are coming from.
Make the most of what you've got. Even if you do a good job of championing UX, you may not have enough time or budget to run a comprehensive research stage, but you can always squeeze in some extra guerrilla testing sessions, extra interviews with friends & family, extra collaborative design workshops with your team members, to apply some techniques that you may not have had the chance to use yet and that may bring some new perspectives to the project.
Document. Take photos of your workspace, your sketches, and other deliverables. Record key web metrics such as conversion rates, number of visitors, and monthly revenue, before the project, and afterwards, so you have solid data on the measurable impact that your project had (this should be happening anyway, but record your own stats, so that you have them to reference down the track when you've moved on from the project or the organisation).
You know, you could always start a blog that captures your team's progress, and your own thoughts and learnings. If your employer is not comfortable with this being out in the open, you could make it an internal blog, for the company staff only.
Hope that helps, and that you enjoy the project!