Ben, unless they've replaced the battery in the Trinnie, I wouldn't take it for any X/Cs unless I was sure I'd be able to get ground power at the other end. I'm reasonably sure it's the battery since it cranks fine on ground power and after a successful start, the charging current to the ships battery is really low, like less than 10 amps, where I expect to see 40+ amps right away with it tapering down quickly.
Albany's a nice flight, even in a 172! I went there in the super-fast-looking-but-not-fast-flying Tampico back in the day when 100 KTAS was about all I could keep up with.