Association CRM with email marketing integration

I'm trying to help a small association that's on a budget get set up with a CRM, webform, and email system. The provider must have been founded at least three years ago — no new companies. Yearly price under $600, fewer than 250 users / 200 households. If an email marketing system isn't built in, it should at least be able to integrate with MailChimp since that's what's currently used. Additional criteria follow. Have already looked at Wix, PayHOA, WildApricot, Member Toolkit, Hubspot, Zoho, and a few others, but none seem like they do this out of the box at this price. Thanks.

1. The system needs to track records by associated household as well as by individuals.
2. The system must offer the ability to collect and track payments offline (by check, by Zelle) and online (Venmo, Stripe, or whatever is built into the system).
3. Ideally, admin would be able to enter offline payments manually in the same field / column as the online payments are tracked. If that's not possible and offline and online payments have to be in separate fields / columns, there still needs to be a way to run a report that shows total amount paid over a specific period of time.
4. Similarly, it needs to offer a report that shows if a household has paid.
5. The email marketing system must be tied to the CRM. When someone updates their name or address in the CRM, it needs to be tied to the same profile the association would use for email marketing, and vice-versa.
6. Automations would be great (household marked as "paid" and receives specific email.