I'd like to get an estimate of total ton-miles per year (i.e., total miles
traveled x tons carried each mile) for liquified natural gas (LNG)
trucks in the US.  Please note that I mean trucks carrying LNG as
cargo, not trucks using LNG for fuel.

Alternatively, I have estimates for total number of LNG shipments and tons
carried for each shipment, so if I could find an estimate for average
miles per shipment, it would get me the estimate I need.

<LNG transport ? mileage.

This report gives statistics for LNG tanker truck accidents and
includes mileage details.

Table 4.12.6-2 on page 154 shows the number of miles travelled by
trucks shipping LNG.
Between 1970 and 1977, 26 million miles were traveled by LNG trucks.
Between 1978 and 2002 it is estimated that 81 million miles were
travelled. The mileage from 1995 to 2002 is based on estimates of
trucking levels.
Over 25 years, 81 million miles were travelled. This gives an average
of 3.24 million miles per year.
Source: Keyspan LNG. Environmental analysis.
http://elibrary.ferc.gov/idmws/common/OpenNat.asp?fileID=10572800

Trucking has been used for the transportation of LNG in North America
since 1970. Well over 100 million LNG truck miles travelled to date.
Between 10,000 and 20,000 truckloads have been delivered in each year.

Source: Terasen Gas.
http://64.233.183.104/search?q=cache:Uk-QlKg2qlIJ:www.terasengas.com/NR/rdonlyres/es6tvolrluysnrlqswq5fo3ggue2g6kt33ry4twlmclvtnbmrs5zf2latvlc5s4wzll3xplym4sw347f3lt37hi6v2b/LNG_ESR_Report.pdf++%22lng+transport%22+trucks++miles&hl=nl&ct=clnk&cd=53

3.24 million miles 
Average of 15,000 truck loads
Gives an average of 216 miles per shipment.>

<Search strategy:>
<"lng shipments" "miles per year" average trucks>
<://www.google.com/search?hl=nl&rls=GGLG%2CGGLG%3A2006-12%2CGGLG%3Aen&q=%22lng+shipments%22+%22miles+per+year%22+average+trucks&lr=>

<"lng transport" trucks  miles>
<://www.google.com/search?q=+%22lng+transport%22+trucks++miles&hl=nl&lr=&rls=GGLG,GGLG:2006-12,GGLG:en&start=50&sa=N>

<Hope this helps.>

This is exactly what I was looking for!  Much appreciated!