Four numbers per case type beat any heat map on your homepage
Until you can see where inquiries stop moving, every improvement is a guess dressed up as a strategy.
Count four things: inquiries received, inquiries where a human made contact, consultations held, matters opened. Split by case type. Nothing more elaborate is needed to find the leak.
Most firms discover the largest drop between the first two. The inquiry arrived and nobody reached the person. That is not a marketing problem and no landing page change will fix it.
Do this manually for a month if the case management system will not report it. A spreadsheet filled in daily by whoever handles intake will teach you more than an analytics dashboard, because it captures what happened on the phone.
Case type matters because the rates differ enormously. A removal inquiry and a naturalization inquiry converting at the same rate would be a strange result, and averaging them hides both.