I'd get a different float.
I have a pretty nice OMER America one that can hold a ton of stuff. Here is a shot of my cheaper Spoarasub float- that you can get from the Deeper BLue store.
I can easily strap on a speargun, water bottle, camera, extra mask, fish stringer- no sharks to worry about around here- and even an occasional anchor that I find. The more stuff you tie on the slower it goes, but even so it still pulls faster than any innertube float.
I wear a D-ring on my belt, threaded through one of my weights, and clip off my float line to it. You can check out the OMER float lines or even make one yourself- there are plenty of threads on here about making your own float line.
Jon