Any "Contact sales" stuff has just been an instant "no" at any company I've ever worked at, because that always means that the numbers are always too high to include in the budget unless it's a directive coming down directly from the top.
A lot of value in some SaaS apps is in the initial investment it took to build it, not in the cost to host a customer's assets.
If the runtime costs of a new customer are negligible, would you rather have 0K or 20K?
If dodgy pricing/sales tactics didn't work then Oracle would be bankrupt instead of a 300 billion dollar company.
Wouldn't surprise me. We had a vendor whose product we had used at relatively reasonable rates for multiple years suddenly have a pricing model change. It would have seen our cost go from $10k/yr to $100k/yr. As a small nonprofit we tried to engage them in any sort of negotiation but the response was essentially a curt "too bad." Luckily a different vendor with a similar product was more than happy to take our $10k.
We have a model that I see a lot of others do, even if they don't publicize. We have free, OSS, and cheap SaaS tiers fine for many of our academic users, and when a small group really wants the full enterprise version, we generally offer a heavily discounted pricing model to make that affordable too. The only exception here is when it is a true enterprise sale like a shared resource for a large number of users, and we'd still have to think there too.
The reason is it keeps their low budgets and thus their ROI in alignment, which is why this is pretty normal. So again, I'd recommend asking and just clarifying your are a NGO/EDU. No 100% guarantee, but should be common.