To me, part of the "thin" sound seemed to be coming from his pick. When I listen to Larry he seemed to always use maybe a medium....medium/heavy pick. You can hear it more so in his tremolo if you really listen, for example the song Tobasco:
http://www.mandolincafe.net/mp3/larryrice-tabasco.mp3
He was definitely a fantastic mandolinist, one of my favs.
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