XF 1.4 Inserting google_analytics / Google Tag Manager after <body>

For a variety of reasons I needed to use Google Tag Manager (GTM) to insert my tracking code instead of straight Google Analytics, so I replaced everything in the google_analytics template with my GTM code. We're seeing some goal attribution issues that might be related to having GTM inserted in the <head>, rather than immediately after opening <body> as recommended by GTM.

What's the best way to get GTM inserted immediately after the opening <body>?