Apollo 10 LM ascent module is indeed in solar orbit, most likely initially in a shorter orbital period then the earth's 365 days.Every 15 years or so a close earth approach, this however presents a possibility of changing Snoopy's solar orbit as described by "Astrogator Mike"
Astrogators guild;Snoopy's future orbits
A NASA history document shows air to ground between transcript of Apollo 10 crew during the mission
Snoopy airlock accidently blows during undocking
Snoopy then fires its engine into solar orbit 23 May 1969.
Archived Apollo 10 LM ascent stage jettison
Listen in to air to ground as crew prepares to jettison Snoopy into solar orbit
Apollo 10 LM ascent stage jettisoned into solar orbit
I have found another great resource of possible ephemerides of Apollo 10 LM ascent stage
Data sheet on Landed LM Landed LM data sheet
Lunar Module impact from orbit data sheet