Automate HubSpot Company Activity Sync

I’m on HubSpot Starter and I can’t get activities logged at the Contact level to surface on the linked Company record. I need a clean, automated way to keep “Company Last Activity Date” and “Company Next Activity Date” fully in-sync with whatever calls, emails, meetings, or tasks my sales team logs under a Contact.

Here’s what I already have and where I’m stuck:
• Segmented views for Hotels, Retail, and Hospitals are in place, but the Company card still shows “No recent activity” unless someone logs it twice.
• HubSpot Starter limits my native automation options, so I’m exploring two angles: (1) the most creative use of filters/reports inside HubSpot, and (2) a Make.com (formerly Integromat) scenario that listens for new Contact engagements and instantly updates the related Company properties.

What I’m expecting from you
1. A workable, documented method to surface Last Activity Date and Next Activity Date on the Company record—either entirely inside HubSpot Starter or with a lightweight Make.com scenario.
2. If Make.com is involved, a ready-to-run scenario (or a clearly outlined blueprint) that I can clone, including any necessary webhooks or API calls.
3. Quick turnaround—ideally within the next few days.

Please tell me about your practical experience with HubSpot Starter limitations and Make.com integrations. A brief outline of similar projects you’ve completed is enough; no lengthy proposals needed.