What are some ways I can leverage partnerships and community sponsorships without a huge budget?

While it generally takes more time, look for ways to find joint go to market opportunities or ways you can partner through a third party to build a relationship. For example, co-sponsorship of an event or partnering as keynote speakers to build mutual brand awareness. If there is something in it for the partner they may be willing to foot the bill for early efforts while your work to demonstrate the value and build up a budget for future collaboration.

Even with a budget cut, you should be able to find ways to leverage partnerships and community. You noted that you have a short list already so I would spend time prioritizing those efforts with the constraint of your new smaller budget. Which ones likely produce the most uplift for you? How much effort/cost is required for each of those? You can then look at the various portfolios of communities and influencers that fit your budget and will bring you the most uplift. That might be 100% to one community, or could be 10 different options each getting 10%. The key is prioritization in a logical way and the following that with focus.

When you think about how to leverage communities and partnerships, I think from a community perspective, look at how you can provide value to the members of the community.

Community should not be about driving direct revenue, it should be a place where you can build brand creditability through your experience, thought leadership, etc. Help to understand what those in the space need and support them through education and partnership vs sales pitches.

Regarding partnership and influences on lower budgets - get creative, and see where you can identify alternative solutions to monetary payment, or if there is a swap component that could provide mutual benefits. One thing I know is that you will never know unless you ask :-)